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Complete non-self-adjacent paths:Results 04A
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a = 5, b = 5
L C S
3 8 2
4 16 4
5 40 10
6 88 22
7 200 46
8 272 66
9 440 100
10 312 76
11 696 132
12 488 116
13 1600 314
14 672 160
15 2616 654
16 496 124
17 112 28
Total 8056 1854
Number of times each node is the start node (SN) in a CNSAP of each length (L)
SN 0 1 2 3 4
5 6 7 8 9
10 11 12 13 14
15 16 17 18 19
20 21 22 23 24
L
3 0 0 0 0 0
0 2 0 2 0
0 0 0 0 0
0 2 0 2 0
0 0 0 0 0
4 0 0 0 0 0
0 0 4 0 0
0 4 0 4 0
0 0 4 0 0
0 0 0 0 0
5 0 0 2 0 0
0 4 0 4 0
2 0 16 0 2
0 4 0 4 0
0 0 2 0 0
6 0 5 0 5 0
5 0 12 0 5
0 12 0 12 0
5 0 12 0 5
0 5 0 5 0
7 10 1 18 1 10
1 18 2 18 1
18 2 0 2 18
1 18 2 18 1
10 1 18 1 10
8 0 31 0 31 0
31 2 4 2 31
0 4 0 4 0
31 2 4 2 31
0 31 0 31 0
9 62 5 24 5 62
5 12 2 12 5
24 2 0 2 24
5 12 2 12 5
62 5 24 5 62
10 6 31 2 31 6
31 2 6 2 31
2 6 0 6 2
31 2 6 2 31
6 31 2 31 6
11 44 18 48 18 44
18 36 10 36 18
48 10 0 10 48
18 36 10 36 18
44 18 48 18 44
12 16 42 6 42 16
42 4 12 4 42
6 12 0 12 6
42 4 12 4 42
16 42 6 42 16
13 82 61 96 61 82
61 76 24 76 61
96 24 0 24 96
61 76 24 76 61
82 61 96 61 82
14 32 56 14 56 32
56 0 10 0 56
14 10 0 10 14
56 0 10 0 56
32 56 14 56 32
15 124 120 184 120 124
120 64 42 64 120
184 42 0 42 184
120 64 42 64 120
124 120 184 120 124
16 40 25 0 25 40
25 0 26 0 25
0 26 32 26 0
25 0 26 0 25
40 25 0 25 40
17 20 0 0 0 20
0 0 0 0 0
0 0 32 0 0
0 0 0 0 0
20 0 0 0 20
Total 436 395 394 395 436
395 220 154 220 395
394 154 80 154 394
395 220 154 220 395
436 395 394 395 436
Grand total = 80 + 4*154 + 4*220 + 4*394 + 8*395 + 4*436
= 8056
Number of times each node is the end node (EN) in a CNSAP of each length (L)
EN 0 1 2 3 4
5 6 7 8 9
10 11 12 13 14
15 16 17 18 19
20 21 22 23 24
L
3 2 0 0 0 2
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
2 0 0 0 2
4 4 0 0 0 4
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
4 0 0 0 4
5 10 0 0 0 10
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
10 0 0 0 10
6 22 0 0 0 22
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
22 0 0 0 22
7 44 2 2 2 44
2 0 0 0 2
2 0 0 0 2
2 0 0 0 2
44 2 2 2 44
8 64 1 2 1 64
1 0 0 0 1
2 0 0 0 2
1 0 0 0 1
64 1 2 1 64
9 90 6 8 6 90
6 0 0 0 6
8 0 0 0 8
6 0 0 0 6
90 6 8 6 90
10 64 5 4 5 64
5 0 0 0 5
4 0 0 0 4
5 0 0 0 5
64 5 4 5 64
11 88 19 32 19 88
19 4 8 4 19
32 8 16 8 32
19 4 8 4 19
88 19 32 19 88
12 80 11 12 11 80
11 0 4 0 11
12 4 16 4 12
11 0 4 0 11
80 11 12 11 80
13 136 57 86 57 136
57 20 32 20 57
86 32 48 32 86
57 20 32 20 57
136 57 86 57 136
14 88 15 22 15 88
15 0 16 0 15
22 16 48 16 22
15 0 16 0 15
88 15 22 15 88
15 160 115 140 115 160
115 56 52 56 115
140 52 64 52 140
115 56 52 56 115
160 115 140 115 160
16 60 15 0 15 60
15 0 18 0 15
0 18 64 18 0
15 0 18 0 15
60 15 0 15 60
17 20 0 0 0 20
0 0 0 0 0
0 0 32 0 0
0 0 0 0 0
20 0 0 0 20
Total 932 246 308 246 932
246 80 130 80 246
308 130 288 130 308
246 80 130 80 246
932 246 308 246 932
Grand total = 4*80 + 4*130 + 8*246 + 288 + 4*308 + 4*932
= 8056
Number of times each node (N) is present in a CNSAP of each length (L)
N 0 1 2 3 4
5 6 7 8 9
10 11 12 13 14
15 16 17 18 19
20 21 22 23 24
L
3 2 1 0 1 2
1 2 0 2 1
0 0 0 0 0
1 2 0 2 1
2 1 0 1 2
4 4 2 0 2 4
2 4 4 4 2
0 4 0 4 0
2 4 4 4 2
4 2 0 2 4
5 10 5 2 5 10
5 14 10 14 5
2 10 16 10 2
5 14 10 14 5
10 5 2 5 10
6 22 16 2 16 22
16 34 34 34 16
2 34 32 34 2
16 34 34 34 16
22 16 2 16 22
7 56 34 30 34 56
34 82 86 82 34
30 86 112 86 30
34 82 86 82 34
56 34 30 34 56
8 68 69 34 69 68
69 124 134 124 69
34 134 184 134 34
69 124 134 124 69
68 69 34 69 68
9 164 116 90 116 164
116 210 220 210 116
90 220 296 220 90
116 210 220 210 116
164 116 90 116 164
10 112 115 82 115 112
115 156 160 156 115
82 160 160 160 82
115 156 160 156 115
112 115 82 115 112
11 210 261 290 261 210
261 428 394 428 261
290 394 280 394 290
261 428 394 428 261
210 261 290 261 210
12 186 242 206 242 186
242 290 248 290 242
206 248 200 248 206
242 290 248 290 242
186 242 206 242 186
13 564 887 1020 887 564
887 956 772 956 887
1020 772 456 772 1020
887 956 772 956 887
564 887 1020 887 564
14 328 428 432 428 328
428 360 320 360 428
432 320 224 320 432
428 360 320 360 428
328 428 432 428 328
15 1284 1945 2344 1945 1284
1945 1232 970 1232 1945
2344 970 360 970 2344
1945 1232 970 1232 1945
1284 1945 2344 1945 1284
16 324 388 434 388 324
388 188 216 188 388
434 216 184 216 434
388 188 216 188 388
324 388 434 388 324
17 92 92 110 92 92
92 24 40 24 92
110 40 104 40 110
92 24 40 24 92
92 92 110 92 92
Total 3426 4601 5076 4601 3426
4601 4104 3608 4104 4601
5076 3608 2608 3608 5076
4601 4104 3608 4104 4601
3426 4601 5076 4601 3426
Grand total = 2608 + 4*3426 + 4*3608 + 4*4104 + 8*4601 + 4*5076
= 104272
Number of CNSAPs for each start node (SN) and end node (EN) pair
SN 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
EN
0 0 0 99 67 64 0 2 19 30 47 99 19 12 18 39 67 30 18 22 40 64 47 39 40 50
1 0 0 0 81 29 78 0 29 3 3 0 0 4 0 3 0 0 0 1 3 2 2 2 3 3
2 74 0 0 0 74 20 60 0 60 20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
3 29 81 0 0 0 3 3 29 0 78 3 0 4 0 0 3 1 0 0 0 3 3 2 2 2
4 64 67 99 0 0 47 30 19 2 0 39 18 12 19 99 40 22 18 30 67 50 40 39 47 64
5 0 78 0 0 2 0 0 0 0 2 0 29 4 0 2 81 3 0 1 3 29 3 3 3 3
6 0 0 40 0 0 0 0 0 0 0 40 0 0 0 0 0 0 0 0 0 0 0 0 0 0
7 13 22 0 22 13 13 0 0 0 13 6 11 0 11 6 0 0 0 0 0 0 0 0 0 0
8 0 0 40 0 0 0 0 0 0 0 0 0 0 0 40 0 0 0 0 0 0 0 0 0 0
9 2 0 0 78 0 2 0 0 0 0 2 0 4 29 0 3 1 0 3 81 3 3 3 3 29
10 74 20 0 0 0 0 60 0 0 0 0 0 0 0 0 0 60 0 0 0 74 20 0 0 0
11 13 13 6 0 0 22 0 11 0 0 0 0 0 0 0 22 0 11 0 0 13 13 6 0 0
12 16 16 16 16 16 16 8 0 8 16 16 0 0 0 16 16 8 0 8 16 16 16 16 16 16
13 0 0 6 13 13 0 0 11 0 22 0 0 0 0 0 0 0 11 0 22 0 0 6 13 13
14 0 0 0 20 74 0 0 0 60 0 0 0 0 0 0 0 0 0 60 0 0 0 0 20 74
15 29 3 3 3 3 81 3 0 1 3 0 29 4 0 2 0 0 0 0 2 0 78 0 0 2
16 0 0 0 0 0 0 0 0 0 0 40 0 0 0 0 0 0 0 0 0 0 0 40 0 0
17 0 0 0 0 0 0 0 0 0 0 6 11 0 11 6 13 0 0 0 13 13 22 0 22 13
18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 40 0 0 0 0 0 0 0 40 0 0
19 3 3 3 3 29 3 1 0 3 81 2 0 4 29 0 2 0 0 0 0 2 0 0 78 0
20 64 47 39 40 50 67 30 18 22 40 99 19 12 18 39 0 2 19 30 47 0 0 99 67 64
21 2 2 2 3 3 0 0 0 1 3 0 0 4 0 3 78 0 29 3 3 0 0 0 81 29
22 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 20 60 0 60 20 74 0 0 0 74
23 3 3 2 2 2 3 1 0 0 0 3 0 4 0 0 3 3 29 0 78 29 81 0 0 0
24 50 40 39 47 64 40 22 18 30 67 39 18 12 19 99 47 30 19 2 0 64 67 99 0 0
Sum of all rows = 4(3*0 + 1*2 + 1*12 + 2*18 + 2*19 + 1*22 + 2*30 + 2*39 + 2*40 + 2*47 + 1*50 + 2*64 + 2*67 + 2*99) +
8(10*0 + 1*1 + 3*2 + 6*3 + 1*4 + 2*29 + 1*78 + 1*81) +
4(19*0 + 2*20 + 2*60 + 2*74) +
4(23*0 + 2*40) +
4(15*0 + 2*6 + 2*11 + 4*13 + 2*22) +
1(5*0 + 4*8 + 16*16)
= 3728 + 1968 + 1232 + 320 + 520 + 288
= 8056
Value repetition frequencies = 4(4*1 + 9*2 + 1*3) +
8(4*1 + 1*2 + 1*3 + 1*6 + 1*10) +
4(3*2 + 1*19) +
4(1*2 + 1*23) +
4(3*2 + 1*4 + 1*15) +
1(1*4 + 1*5 + 1*16)
= 625
Number of distinct row element sets = 6
Number of rows = 1*1 + 4*4 + 1*8
= 25
Number of distinct values = 28
Distinct values 0 1 2 3 4 6 8 11 12 13 16 18 19 20 22 29 30 39 40 47 50 60 64 67 74 78 81 99
Frequency 325 8 28 48 8 8 4 8 4 16 16 8 8 8 12 16 8 8 16 8 4 8 8 8 8 8 8 8
Sum of distinct value frequencies = 3*4 + 17*8 + 1*12 + 4*16 + 1*28 + 1*48 + 1*325
= 625
Number of SN-EN pairs for which the number of CNSAPs is greater than zero = 4*2 + 4*6 + 4*10 + 8*15 + 1*20 + 4*22
= 300
Number of SN-EN pairs, with SN != EN, for which the number of CNSAPs equals zero = 300
Number of possible SN-EN pairs with SN != EN = 25*24
= 600
a = 6, b = 5
L C S
3 8 2
4 16 4
5 40 10
6 88 22
7 212 50
8 344 100
9 644 192
10 820 318
11 1224 340
12 1204 430
13 2924 726
14 2244 816
15 6480 1786
16 3424 1454
17 9364 4626
18 2788 1394
19 1412 706
20 436 218
21 8 4
Total 33680 13198
Number of times each node is the start node (SN) in a CNSAP of each length (L)
SN 0 1 2 3 4 5
6 7 8 9 10 11
12 13 14 15 16 17
18 19 20 21 22 23
24 25 26 27 28 29
L
3 0 0 0 0 0 0
0 2 0 0 2 0
0 0 0 0 0 0
0 2 0 0 2 0
0 0 0 0 0 0
4 0 0 0 0 0 0
0 0 2 2 0 0
0 4 0 0 4 0
0 0 2 2 0 0
0 0 0 0 0 0
5 0 0 1 1 0 0
0 2 2 2 2 0
2 0 8 8 0 2
0 2 2 2 2 0
0 0 1 1 0 0
6 0 2 3 3 2 0
3 2 6 6 2 3
0 0 12 12 0 0
3 2 6 6 2 3
0 2 3 3 2 0
7 5 6 9 9 6 5
3 4 16 16 4 3
2 18 0 0 18 2
3 4 16 16 4 3
5 6 9 9 6 5
8 7 8 23 23 8 7
4 29 3 3 29 4
20 0 4 4 0 20
4 29 3 3 29 4
7 8 23 23 8 7
9 13 54 14 14 54 13
51 7 9 9 7 51
6 20 0 0 20 6
51 7 9 9 7 51
13 54 14 14 54 13
10 97 16 19 19 16 97
10 27 4 4 27 10
56 2 6 6 2 56
10 27 4 4 27 10
97 16 19 19 16 97
11 33 52 34 34 52 33
93 29 29 29 29 93
26 42 4 4 42 26
93 29 29 29 29 93
33 52 34 34 52 33
12 75 32 42 42 32 75
30 48 11 11 48 30
106 6 14 14 6 106
30 48 11 11 48 30
75 32 42 42 32 75
13 76 143 109 109 143 76
142 89 75 75 89 142
98 88 8 8 88 98
142 89 75 75 89 142
76 143 109 109 143 76
14 143 64 106 106 64 143
88 77 26 26 77 88
76 24 14 14 24 76
88 77 26 26 77 88
143 64 106 106 64 143
15 196 322 297 297 322 196
234 208 138 138 208 234
296 144 10 10 144 296
234 208 138 138 208 234
196 322 297 297 322 196
16 202 126 165 165 126 202
188 30 50 50 30 188
114 30 46 46 30 114
188 30 50 50 30 188
202 126 165 165 126 202
17 386 338 470 470 338 386
397 236 151 151 236 397
536 164 26 26 164 536
397 236 151 151 236 397
386 338 470 470 338 386
18 177 118 56 56 118 177
141 15 98 98 15 141
32 54 98 98 54 32
141 15 98 98 15 141
177 118 56 56 118 177
19 130 65 17 17 65 130
26 8 32 32 8 26
32 0 118 118 0 32
26 8 32 32 8 26
130 65 17 17 65 130
20 39 34 0 0 34 39
4 0 0 0 0 4
0 0 64 64 0 0
4 0 0 0 0 4
39 34 0 0 34 39
21 1 1 0 0 1 1
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
1 1 0 0 1 1
Total 1580 1381 1365 1365 1381 1580
1414 813 652 652 813 1414
1402 596 432 432 596 1402
1414 813 652 652 813 1414
1580 1381 1365 1365 1381 1580
Grand total = 2*432 + 2*596 + 4*652 + 4*813 + 4*1365 + 4*1381 + 2*1402 + 4*1414 + 4*1580
= 33680
Number of times each node is the end node (EN) in a CNSAP of each length (L)
EN 0 1 2 3 4 5
6 7 8 9 10 11
12 13 14 15 16 17
18 19 20 21 22 23
24 25 26 27 28 29
L
3 2 0 0 0 0 2
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
2 0 0 0 0 2
4 4 0 0 0 0 4
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
4 0 0 0 0 4
5 10 0 0 0 0 10
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
10 0 0 0 0 10
6 22 0 0 0 0 22
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
22 0 0 0 0 22
7 46 2 2 2 2 46
2 0 0 0 0 2
2 0 0 0 0 2
2 0 0 0 0 2
46 2 2 2 2 46
8 81 1 2 2 1 81
1 0 0 0 0 1
2 0 0 0 0 2
1 0 0 0 0 1
81 1 2 2 1 81
9 136 6 9 9 6 136
6 0 0 0 0 6
8 0 0 0 0 8
6 0 0 0 0 6
136 6 9 9 6 136
10 184 6 8 8 6 184
5 0 0 0 0 5
4 0 0 0 0 4
5 0 0 0 0 5
184 6 8 8 6 184
11 185 25 37 37 25 185
19 4 8 8 4 19
32 8 16 16 8 32
19 4 8 8 4 19
185 25 37 37 25 185
12 226 17 27 27 17 226
11 0 4 4 0 11
12 4 16 16 4 12
11 0 4 4 0 11
226 17 27 27 17 226
13 310 76 125 125 76 310
60 20 44 44 20 60
88 32 72 72 32 88
60 20 44 44 20 60
310 76 125 125 76 310
14 346 32 72 72 32 346
19 0 30 30 0 19
24 16 84 84 16 24
19 0 30 30 0 19
346 32 72 72 32 346
15 476 193 320 320 193 476
168 72 144 144 72 168
230 84 180 180 84 230
168 72 144 144 72 168
476 193 320 320 193 476
16 402 59 134 134 59 402
43 0 81 81 0 43
42 30 202 202 30 42
43 0 81 81 0 43
402 59 134 134 59 402
17 553 357 375 375 357 553
326 155 180 180 155 326
412 152 226 226 152 412
326 155 180 180 155 326
553 357 375 375 357 553
18 269 105 51 51 105 269
70 0 69 69 0 70
32 26 208 208 26 32
70 0 69 69 0 70
269 105 51 51 105 269
19 139 78 17 17 78 139
12 0 20 20 0 12
32 0 142 142 0 32
12 0 20 20 0 12
139 78 17 17 78 139
20 39 34 0 0 34 39
4 0 0 0 0 4
0 0 64 64 0 0
4 0 0 0 0 4
39 34 0 0 34 39
21 1 1 0 0 1 1
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
1 1 0 0 1 1
Total 3431 992 1179 1179 992 3431
746 251 580 580 251 746
920 352 1210 1210 352 920
746 251 580 580 251 746
3431 992 1179 1179 992 3431
Grand total = 4*251 + 2*352 + 4*580 + 4*746 + 2*920 + 4*992 + 4*1179 + 2*1210 + 4*3431
= 33680
Number of times each node (N) is present in a CNSAP of each length (L)
N 0 1 2 3 4 5
6 7 8 9 10 11
12 13 14 15 16 17
18 19 20 21 22 23
24 25 26 27 28 29
L
3 2 1 0 0 1 2
1 2 0 0 2 1
0 0 0 0 0 0
1 2 0 0 2 1
2 1 0 0 1 2
4 4 2 0 0 2 4
2 4 2 2 4 2
0 4 0 0 4 0
2 4 2 2 4 2
4 2 0 0 2 4
5 10 5 1 1 5 10
5 12 7 7 12 5
2 10 8 8 10 2
5 12 7 7 12 5
10 5 1 1 5 10
6 22 13 4 4 13 22
14 30 23 23 30 14
2 22 28 28 22 2
14 30 23 23 30 14
22 13 4 4 13 22
7 53 37 20 20 37 53
33 66 73 73 66 33
14 74 90 90 74 14
33 66 73 73 66 33
53 37 20 20 37 53
8 91 59 47 47 59 91
53 136 139 139 136 53
30 118 178 178 118 30
53 136 139 139 136 53
91 59 47 47 59 91
9 163 156 100 100 156 163
149 255 267 267 255 149
76 260 382 382 260 76
149 255 267 267 255 149
163 156 100 100 156 163
10 304 220 132 132 220 304
193 382 346 346 382 193
124 366 456 456 366 124
193 382 346 346 382 193
304 220 132 132 220 304
11 323 354 365 365 354 323
375 552 654 654 552 375
320 548 618 618 548 320
375 552 654 654 552 375
323 354 365 365 354 323
12 409 403 382 382 403 409
405 669 578 578 669 405
366 622 544 544 622 366
405 669 578 578 669 405
409 403 382 382 403 409
13 774 1182 1423 1423 1182 774
1081 1566 1539 1539 1566 1081
1146 1518 1212 1212 1518 1146
1081 1566 1539 1539 1566 1081
774 1182 1423 1423 1182 774
14 831 1014 1111 1111 1014 831
999 1321 1061 1061 1321 999
956 1204 874 874 1204 956
999 1321 1061 1061 1321 999
831 1014 1111 1111 1014 831
15 1967 3481 4308 4308 3481 1967
3090 3867 3009 3009 3867 3090
3598 3698 1860 1860 3698 3598
3090 3867 3009 3009 3867 3090
1967 3481 4308 4308 3481 1967
16 1486 1972 2254 2254 1972 1486
1948 1887 1619 1619 1887 1948
2092 1784 1184 1184 1784 2092
1948 1887 1619 1619 1887 1948
1486 1972 2254 2254 1972 1486
17 4108 5955 7515 7515 5955 4108
6710 4644 3907 3907 4644 6710
8196 3940 1780 1780 3940 8196
6710 4644 3907 3907 4644 6710
4108 5955 7515 7515 5955 4108
18 1548 1946 2173 2173 1946 1548
2154 1277 1241 1241 1277 2154
2380 1120 914 914 1120 2380
2154 1277 1241 1241 1277 2154
1548 1946 2173 2173 1946 1548
19 916 1105 1118 1118 1105 916
1128 564 640 640 564 1128
1320 484 668 668 484 1320
1128 564 640 640 564 1128
916 1105 1118 1118 1105 916
20 325 389 350 350 389 325
380 128 164 164 128 380
420 120 348 348 120 420
380 128 164 164 128 380
325 389 350 350 389 325
21 8 8 4 4 8 8
6 2 6 6 2 6
8 4 4 4 4 8
6 2 6 6 2 6
8 8 4 4 8 8
Total 13344 18302 21307 21307 18302 13344
18726 17364 15275 15275 17364 18726
21050 15896 11148 11148 15896 21050
18726 17364 15275 15275 17364 18726
13344 18302 21307 21307 18302 13344
Grand total = 2*11148 + 4*13344 + 4*15275 + 2*15896 + 4*17364 + 4*18302 + 4*18726 + 2*21050 + 4*21307
= 513460
Number of CNSAPs for each start node (SN) and end node (EN) pair
SN 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29
EN
0 0 0 304 239 214 212 0 2 79 113 108 154 284 45 43 60 61 122 213 101 57 47 62 115 206 141 103 98 111 137
1 0 0 0 253 37 40 225 0 90 56 3 29 0 0 30 16 6 24 0 0 0 7 17 27 13 13 13 24 36 33
2 217 0 0 0 260 114 78 195 0 138 20 20 0 0 8 22 0 20 2 0 0 0 6 20 4 4 4 8 19 20
3 114 260 0 0 0 217 20 20 138 0 195 78 20 0 22 8 0 0 20 6 0 0 0 2 20 19 8 4 4 4
4 40 37 253 0 0 0 29 3 56 90 0 225 24 6 16 30 0 0 27 17 7 0 0 0 33 36 24 13 13 13
5 212 214 239 304 0 0 154 108 113 79 2 0 122 61 60 43 45 284 115 62 47 57 101 213 137 111 98 103 141 206
6 0 225 0 0 11 12 0 0 0 0 6 9 0 99 17 4 3 7 220 8 0 1 3 6 88 8 6 4 4 5
7 0 0 117 0 0 0 0 0 0 0 0 0 134 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
8 74 65 0 96 36 37 74 0 0 0 30 19 40 66 0 16 6 6 0 0 0 0 0 6 0 0 0 0 3 6
9 37 36 96 0 65 74 19 30 0 0 0 74 6 6 16 0 66 40 6 0 0 0 0 0 6 3 0 0 0 0
10 0 0 0 117 0 0 0 0 0 0 0 0 0 0 0 0 0 134 0 0 0 0 0 0 0 0 0 0 0 0
11 12 11 0 0 225 0 9 6 0 0 0 0 7 3 4 17 99 0 6 3 1 0 8 220 5 4 4 6 8 88
12 210 58 0 0 0 0 0 192 0 0 0 0 0 0 0 0 0 0 0 192 0 0 0 0 210 58 0 0 0 0
13 26 26 12 0 0 0 74 0 38 0 0 0 0 0 0 0 0 0 74 0 38 0 0 0 26 26 12 0 0 0
14 70 70 46 38 40 56 79 36 0 26 24 44 88 0 0 0 24 40 79 36 0 26 24 44 70 70 46 38 40 56
15 56 40 38 46 70 70 44 24 26 0 36 79 40 24 0 0 0 88 44 24 26 0 36 79 56 40 38 46 70 70
16 0 0 0 12 26 26 0 0 0 38 0 74 0 0 0 0 0 0 0 0 0 38 0 74 0 0 0 12 26 26
17 0 0 0 0 58 210 0 0 0 0 192 0 0 0 0 0 0 0 0 0 0 0 192 0 0 0 0 0 58 210
18 88 8 6 4 4 5 220 8 0 1 3 6 0 99 17 4 3 7 0 0 0 0 6 9 0 225 0 0 11 12
19 0 0 0 0 0 0 0 0 0 0 0 0 134 0 0 0 0 0 0 0 0 0 0 0 0 0 117 0 0 0
20 0 0 0 0 3 6 0 0 0 0 0 6 40 66 0 16 6 6 74 0 0 0 30 19 74 65 0 96 36 37
21 6 3 0 0 0 0 6 0 0 0 0 0 6 6 16 0 66 40 19 30 0 0 0 74 37 36 96 0 65 74
22 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 134 0 0 0 0 0 0 0 0 0 117 0 0
23 5 4 4 6 8 88 6 3 1 0 8 220 7 3 4 17 99 0 9 6 0 0 0 0 12 11 0 0 225 0
24 206 141 103 98 111 137 213 101 57 47 62 115 284 45 43 60 61 122 0 2 79 113 108 154 0 0 304 239 214 212
25 13 13 13 24 36 33 0 0 0 7 17 27 0 0 30 16 6 24 225 0 90 56 3 29 0 0 0 253 37 40
26 4 4 4 8 19 20 2 0 0 0 6 20 0 0 8 22 0 20 78 195 0 138 20 20 217 0 0 0 260 114
27 20 19 8 4 4 4 20 6 0 0 0 2 20 0 22 8 0 0 20 20 138 0 195 78 114 260 0 0 0 217
28 33 36 24 13 13 13 27 17 7 0 0 0 24 6 16 30 0 0 29 3 56 90 0 225 40 37 253 0 0 0
29 137 111 98 103 141 206 115 62 47 57 101 213 122 61 60 43 45 284 154 108 113 79 2 0 212 214 239 304 0 0
Sum of all rows = 4(3*0 + 1*2 + 1*43 + 1*45 + 1*47 + 1*57 + 1*60 + 1*61 + 1*62 + 1*79 + 1*98 + 1*101 + 1*103 + 1*108 + 1*111 + 1*113 + 1*115 + 1*122 + 1*137 + 1*141 + 1*154 + 1*206 + 1*212 + 1*213 + 1*214 +
1*239 + 1*284 + 1*304) +
4(9*0 + 1*3 + 1*6 + 1*7 + 3*13 + 1*16 + 1*17 + 2*24 + 1*27 + 1*29 + 1*30 + 1*33 + 1*36 + 1*37 + 1*40 + 1*56 + 1*90 + 1*225 + 1*253) +
4(10*0 + 1*2 + 3*4 + 1*6 + 2*8 + 1*19 + 5*20 + 1*22 + 1*78 + 1*114 + 1*138 + 1*195 + 1*217 + 1*260) +
4(9*0 + 1*1 + 2*3 + 3*4 + 1*5 + 3*6 + 1*7 + 2*8 + 1*9 + 1*11 + 1*12 + 1*17 + 1*88 + 1*99 + 1*220 + 1*225) +
4(28*0 + 1*117 + 1*134) +
4(14*0 + 1*3 + 4*6 + 1*16 + 1*19 + 1*30 + 1*36 + 1*37 + 1*40 + 1*65 + 1*66 + 2*74 + 1*96) +
2(24*0 + 2*58 + 2*192 + 2*210) +
2(20*0 + 2*12 + 4*26 + 2*38 + 2*74) +
2(5*0 + 3*24 + 2*26 + 2*36 + 2*38 + 3*40 + 2*44 + 2*46 + 2*56 + 4*70 + 2*79 + 1*88)
= 13724 + 3968 + 4716 + 2984 + 1004 + 2320 + 1840 + 704 + 2420
= 33680
Value repetition frequencies = 4(27*1 + 1*3) +
4(16*1 + 1*2 + 1*3 + 1*9) +
4(10*1 + 1*2 + 1*3 + 1*5 + 1*10) +
4(11*1 + 2*2 + 2*3 + 1*9) +
4(2*1 + 1*28) +
4(10*1 + 1*2 + 1*4 + 1*14) +
2(3*2 + 1*24) +
2(3*2 + 1*4 + 1*20) +
2(1*1 + 7*2 + 2*3 + 1*4 + 1*5)
= 900
Number of distinct row element sets = 9
Number of rows = 3*2 + 6*4
= 30
Number of distinct values = 79
Distinct values 0 1 2 3 4 5 6 7 8 9 11 12 13 16 17 19 20 22 24 26 27 29 30 33 36
Frequency 390 4 8 16 24 4 36 8 16 4 4 8 12 8 8 8 20 4 14 12 4 4 8 4 12
Distinct values 37 38 40 43 44 45 46 47 56 57 58 60 61 62 65 66 70 74 78 79 88 90 96 98 99
Frequency 8 8 14 4 4 4 4 4 8 4 4 4 4 4 4 4 8 12 4 8 6 4 4 4 4
Distinct values 101 103 108 111 113 114 115 117 122 134 137 138 141 154 192 195 206 210 212 213 214 217 220 225 239
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 8 4
Distinct values 253 260 284 304
Frequency 4 4 4 4
Sum of distinct value frequencies = 53*4 + 1*6 + 13*8 + 4*12 + 2*14 + 2*16 + 1*20 + 1*24 + 1*36 + 1*390
= 900
Number of SN-EN pairs for which the number of CNSAPs is greater than zero = 4*2 + 2*6 + 2*10 + 4*16 + 4*20 + 8*21 + 2*25 + 4*27
= 510
Number of SN-EN pairs, with SN != EN, for which the number of CNSAPs equals zero = 360
Number of possible SN-EN pairs with SN != EN = 29*30
= 870
a = 7, b = 5
L C S
3 8 2
4 16 4
5 40 10
6 88 22
7 216 50
8 356 104
9 748 234
10 1132 460
11 2240 778
12 2264 894
13 5164 1540
14 4764 1812
15 12084 3444
16 9132 3512
17 22368 8294
18 13768 6104
19 28780 13914
20 11828 5778
21 11100 5548
22 4432 2216
23 1420 710
24 48 24
Total 131996 55454
Number of times each node is the start node (SN) in a CNSAP of each length (L)
SN 0 1 2 3 4 5 6
7 8 9 10 11 12 13
14 15 16 17 18 19 20
21 22 23 24 25 26 27
28 29 30 31 32 33 34
L
3 0 0 0 0 0 0 0
0 2 0 0 0 2 0
0 0 0 0 0 0 0
0 2 0 0 0 2 0
0 0 0 0 0 0 0
4 0 0 0 0 0 0 0
0 0 2 0 2 0 0
0 4 0 0 0 4 0
0 0 2 0 2 0 0
0 0 0 0 0 0 0
5 0 0 1 0 1 0 0
0 2 0 4 0 2 0
2 0 8 0 8 0 2
0 2 0 4 0 2 0
0 0 1 0 1 0 0
6 0 2 0 6 0 2 0
3 0 8 0 8 0 3
0 0 0 24 0 0 0
3 0 8 0 8 0 3
0 2 0 6 0 2 0
7 5 1 14 0 14 1 5
1 6 2 30 2 6 1
2 2 16 0 16 2 2
1 6 2 30 2 6 1
5 1 14 0 14 1 5
8 0 15 0 46 0 15 0
6 2 30 2 30 2 6
0 20 0 8 0 20 0
6 2 30 2 30 2 6
0 15 0 46 0 15 0
9 22 5 63 4 63 5 22
5 53 4 16 4 53 5
30 2 18 0 18 2 30
5 53 4 16 4 53 5
22 5 63 4 63 5 22
10 6 107 4 36 4 107 6
81 4 29 2 29 4 81
2 56 2 12 2 56 2
81 4 29 2 29 4 81
6 107 4 36 4 107 6
11 187 23 68 20 68 23 187
20 106 20 48 20 106 20
150 14 36 8 36 14 150
20 106 20 48 20 106 20
187 23 68 20 68 23 187
12 23 113 14 78 14 113 23
225 17 57 6 57 17 225
14 116 6 28 6 116 14
225 17 57 6 57 17 225
23 113 14 78 14 113 23
13 258 89 212 86 212 89 258
82 208 69 130 69 208 82
388 58 76 16 76 58 388
82 208 69 130 69 208 82
258 89 212 86 212 89 258
14 75 283 39 242 39 283 75
343 60 137 2 137 60 343
72 160 16 32 16 160 72
343 60 137 2 137 60 343
75 283 39 242 39 283 75
15 549 269 631 288 631 269 549
267 434 172 302 172 434 267
448 220 130 20 130 220 448
267 434 172 302 172 434 267
549 269 631 288 631 269 549
16 246 570 78 606 78 570 246
417 142 271 26 271 142 417
250 156 30 100 30 156 250
417 142 271 26 271 142 417
246 570 78 606 78 570 246
17 810 579 1238 660 1238 579 810
660 665 249 582 249 665 660
906 468 156 20 156 468 906
660 665 249 582 249 665 660
810 579 1238 660 1238 579 810
18 569 554 161 932 161 554 569
763 116 336 148 336 116 763
454 110 88 308 88 110 454
763 116 336 148 336 116 763
569 554 161 932 161 554 569
19 1246 792 1161 980 1161 792 1246
1029 709 348 660 348 709 1029
1436 434 244 132 244 434 1436
1029 709 348 660 348 709 1029
1246 792 1161 980 1161 792 1246
20 572 567 258 172 258 567 572
585 98 256 334 256 98 585
104 130 226 552 226 130 104
585 98 256 334 256 98 585
572 567 258 172 258 567 572
21 732 457 298 178 298 457 732
230 160 228 238 228 160 230
358 48 276 484 276 48 358
230 160 228 238 228 160 230
732 457 298 178 298 457 732
22 209 333 118 70 118 333 209
95 4 36 12 36 4 95
0 36 276 464 276 36 0
95 4 36 12 36 4 95
209 333 118 70 118 333 209
23 89 33 93 8 93 33 89
17 4 29 14 29 4 17
34 0 104 40 104 0 34
17 4 29 14 29 4 17
89 33 93 8 93 33 89
24 2 3 2 0 2 3 2
0 0 2 0 2 0 0
0 2 4 0 4 2 0
0 0 2 0 2 0 0
2 3 2 0 2 3 2
Total 5600 4795 4453 4412 4453 4795 5600
4829 2792 2285 2556 2285 2792 4829
4650 2036 1712 2248 1712 2036 4650
4829 2792 2285 2556 2285 2792 4829
5600 4795 4453 4412 4453 4795 5600
Grand total = 2*1712 + 2*2036 + 2248 + 4*2285 + 2*2556 + 4*2792 + 2*4412 + 4*4453 + 2*4650 + 4*4795 + 4*4829 + 4*5600
= 131996
Number of times each node is the end node (EN) in a CNSAP of each length (L)
EN 0 1 2 3 4 5 6
7 8 9 10 11 12 13
14 15 16 17 18 19 20
21 22 23 24 25 26 27
28 29 30 31 32 33 34
L
3 2 0 0 0 0 0 2
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
2 0 0 0 0 0 2
4 4 0 0 0 0 0 4
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
4 0 0 0 0 0 4
5 10 0 0 0 0 0 10
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
10 0 0 0 0 0 10
6 22 0 0 0 0 0 22
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
22 0 0 0 0 0 22
7 46 2 2 2 2 2 46
2 0 0 0 0 0 2
2 0 0 0 0 0 2
2 0 0 0 0 0 2
46 2 2 2 2 2 46
8 83 1 2 2 2 1 83
1 0 0 0 0 0 1
2 0 0 0 0 0 2
1 0 0 0 0 0 1
83 1 2 2 2 1 83
9 157 6 9 10 9 6 157
6 0 0 0 0 0 6
8 0 0 0 0 0 8
6 0 0 0 0 0 6
157 6 9 10 9 6 157
10 255 6 9 12 9 6 255
5 0 0 0 0 0 5
4 0 0 0 0 0 4
5 0 0 0 0 0 5
255 6 9 12 9 6 255
11 403 26 43 42 43 26 403
19 4 8 8 8 4 19
32 8 16 16 16 8 32
19 4 8 8 8 4 19
403 26 43 42 43 26 403
12 449 25 34 42 34 25 449
11 0 4 4 4 0 11
12 4 16 16 16 4 12
11 0 4 4 4 0 11
449 25 34 42 34 25 449
13 697 89 150 166 150 89 697
60 20 44 56 44 20 60
88 32 72 96 72 32 88
60 20 44 56 44 20 60
697 89 150 166 150 89 697
14 794 64 100 130 100 64 794
20 0 32 44 32 0 20
24 16 88 120 88 16 24
20 0 32 44 32 0 20
794 64 100 130 100 64 794
15 1184 236 440 526 440 236 1184
174 72 172 248 172 72 174
232 84 236 320 236 84 232
174 72 172 248 172 72 174
1184 236 440 526 440 236 1184
16 1163 135 242 360 242 135 1163
57 0 123 192 123 0 57
44 30 282 436 282 30 44
57 0 123 192 123 0 57
1163 135 242 360 242 135 1163
17 1617 525 937 918 937 525 1617
416 177 402 508 402 177 416
546 196 554 628 554 196 546
416 177 402 508 402 177 416
1617 525 937 918 937 525 1617
18 1350 281 413 566 413 281 1350
138 0 249 384 249 0 138
102 42 490 876 490 42 102
138 0 249 384 249 0 138
1350 281 413 566 413 281 1350
19 1756 950 1051 816 1051 950 1756
742 329 417 612 417 329 742
1012 358 676 852 676 358 1012
742 329 417 612 417 329 742
1756 950 1051 816 1051 950 1756
20 936 437 321 276 321 437 936
211 0 226 176 226 0 211
164 56 540 880 540 56 164
211 0 226 176 226 0 211
936 437 321 276 321 437 936
21 740 471 381 230 381 471 740
199 34 189 132 189 34 199
292 86 518 528 518 86 292
199 34 189 132 189 34 199
740 471 381 230 381 471 740
22 269 233 170 64 170 233 269
65 0 44 16 44 0 65
16 38 356 328 356 38 16
65 0 44 16 44 0 65
269 233 170 64 170 233 269
23 88 32 93 8 93 32 88
17 4 29 14 29 4 17
32 2 108 40 108 2 32
17 4 29 14 29 4 17
88 32 93 8 93 32 88
24 2 3 2 0 2 3 2
0 0 2 0 2 0 0
0 2 4 0 4 2 0
0 0 2 0 2 0 0
2 3 2 0 2 3 2
Total 12027 3522 4399 4170 4399 3522 12027
2143 640 1941 2394 1941 640 2143
2612 954 3956 5136 3956 954 2612
2143 640 1941 2394 1941 640 2143
12027 3522 4399 4170 4399 3522 12027
Grand total = 4*640 + 2*954 + 4*1941 + 4*2143 + 2*2394 + 2*2612 + 4*3522 + 2*3956 + 2*4170 + 4*4399 + 5136 + 4*12027
= 131996
Number of times each node (N) is present in a CNSAP of each length (L)
N 0 1 2 3 4 5 6
7 8 9 10 11 12 13
14 15 16 17 18 19 20
21 22 23 24 25 26 27
28 29 30 31 32 33 34
L
3 2 1 0 0 0 1 2
1 2 0 0 0 2 1
0 0 0 0 0 0 0
1 2 0 0 0 2 1
2 1 0 0 0 1 2
4 4 2 0 0 0 2 4
2 4 2 0 2 4 2
0 4 0 0 0 4 0
2 4 2 0 2 4 2
4 2 0 0 0 2 4
5 10 5 1 0 1 5 10
5 12 5 4 5 12 5
2 10 8 0 8 10 2
5 12 5 4 5 12 5
10 5 1 0 1 5 10
6 22 13 1 6 1 13 22
14 28 19 12 19 28 14
2 22 16 24 16 22 2
14 28 19 12 19 28 14
22 13 1 6 1 13 22
7 53 32 22 10 22 32 53
31 62 53 56 53 62 31
14 58 78 68 78 58 14
31 62 53 56 53 62 31
53 32 22 10 22 32 53
8 86 61 26 58 26 61 86
52 107 126 118 126 107 52
10 98 146 156 146 98 10
52 107 126 118 126 107 52
86 61 26 58 26 61 86
9 190 122 120 112 120 122 190
116 260 265 274 265 260 116
68 218 354 388 354 218 68
116 260 265 274 265 260 116
190 122 120 112 120 122 190
10 286 280 161 172 161 280 286
237 437 445 420 445 437 237
74 420 568 628 568 420 74
237 437 445 420 445 437 237
286 280 161 172 161 280 286
11 656 521 444 462 444 521 656
473 934 921 1050 921 934 473
388 834 1050 1276 1050 834 388
473 934 921 1050 921 934 473
656 521 444 462 444 521 656
12 621 630 527 628 527 630 621
640 1042 1024 1002 1024 1042 640
360 1076 1050 1000 1050 1076 360
640 1042 1024 1002 1024 1042 640
621 630 527 628 527 630 621
13 1346 1490 1803 1962 1803 1490 1346
1418 2347 2464 2624 2464 2347 1418
1466 2274 2360 2288 2360 2274 1466
1418 2347 2464 2624 2464 2347 1418
1346 1490 1803 1962 1803 1490 1346
14 1346 1682 1731 2038 1731 1682 1346
1623 2455 2300 2046 2300 2455 1623
1414 2504 2150 1844 2150 2504 1414
1623 2455 2300 2046 2300 2455 1623
1346 1682 1731 2038 1731 1682 1346
15 3172 4543 6275 6666 6275 4543 3172
4079 6104 6125 5548 6125 6104 4079
4402 6042 5350 4052 5350 6042 4402
4079 6104 6125 5548 6125 6104 4079
3172 4543 6275 6666 6275 4543 3172
16 2926 4083 4416 5080 4416 4083 2926
3819 4996 4543 4138 4543 4996 3819
3864 4890 3850 3336 3850 4890 3864
3819 4996 4543 4138 4543 4996 3819
2926 4083 4416 5080 4416 4083 2926
17 6482 11009 14055 14934 14055 11009 6482
9826 13229 10390 10070 10390 13229 9826
11522 13462 7418 5480 7418 13462 11522
9826 13229 10390 10070 10390 13229 9826
6482 11009 14055 14934 14055 11009 6482
18 5244 7373 8519 9522 8519 7373 5244
7442 7570 6571 6292 6571 7570 7442
8022 7338 4976 4648 4976 7338 8022
7442 7570 6571 6292 6571 7570 7442
5244 7373 8519 9522 8519 7373 5244
19 11789 16428 20421 21754 20421 16428 11789
19610 14773 12702 12682 12702 14773 19610
24064 13166 7370 5856 7370 13166 24064
19610 14773 12702 12682 12702 14773 19610
11789 16428 20421 21754 20421 16428 11789
20 5708 7650 8416 8660 8416 7650 5708
8751 6007 5224 5512 5224 6007 8751
9802 4942 3564 4576 3564 4942 9802
8751 6007 5224 5512 5224 6007 8751
5708 7650 8416 8660 8416 7650 5708
21 6230 8025 8434 7180 8434 8025 6230
8644 5090 5599 5722 5599 5090 8644
10200 3932 3322 4300 3322 3932 10200
8644 5090 5599 5722 5599 5090 8644
6230 8025 8434 7180 8434 8025 6230
22 2777 3708 3549 3022 3549 3708 2777
3679 1777 1745 2018 1745 1777 3679
4156 1536 1996 3108 1996 1536 4156
3679 1777 1745 2018 1745 1777 3679
2777 3708 3549 3022 3549 3708 2777
23 1042 1323 1300 664 1300 1323 1042
1230 430 668 500 668 430 1230
1398 314 892 1152 892 314 1398
1230 430 668 500 668 430 1230
1042 1323 1300 664 1300 1323 1042
24 44 48 42 12 42 48 44
44 4 38 28 38 4 44
48 8 32 16 32 8 48
44 4 38 28 38 4 44
44 48 42 12 42 48 44
Total 50036 69029 80263 82942 80263 69029 50036
71736 67670 61229 60116 61229 67670 71736
81276 63148 46550 44196 46550 63148 81276
71736 67670 61229 60116 61229 67670 71736
50036 69029 80263 82942 80263 69029 50036
Grand total = 44196 + 2*46550 + 4*50036 + 2*60116 + 4*61229 + 2*63148 + 4*67670 + 4*69029 + 4*71736 + 4*80263 + 2*81276 + 2*82942
= 2312112
Number of CNSAPs for each start node (SN) and end node (EN) pair
SN 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34
EN
0 0 0 833 697 653 559 607 0 2 225 396 352 289 446 792 107 109 237 207 184 371 670 318 187 140 152 219 378 669 454 307 269 322 410 466
1 0 0 0 658 45 57 60 607 0 291 232 3 29 75 0 0 120 88 53 45 88 0 0 0 33 86 90 115 49 49 49 98 171 165 166
2 594 0 0 0 752 134 154 225 513 0 396 166 20 114 0 0 52 145 40 40 114 13 0 0 0 42 102 134 26 26 26 52 143 202 174
3 339 644 0 0 0 644 339 82 78 414 0 414 78 82 82 0 70 68 70 0 82 84 31 0 0 0 31 84 84 91 42 20 42 91 84
4 154 134 752 0 0 0 594 114 20 166 396 0 513 225 114 40 40 145 52 0 0 134 102 42 0 0 0 13 174 202 143 52 26 26 26
5 60 57 45 658 0 0 0 75 29 3 232 291 0 607 88 45 53 88 120 0 0 115 90 86 33 0 0 0 166 165 171 98 49 49 49
6 607 559 653 697 833 0 0 446 289 352 396 225 2 0 371 184 207 237 109 107 792 378 219 152 140 187 318 670 466 410 322 269 307 454 669
7 0 607 0 0 31 36 40 0 0 0 0 19 18 28 0 284 43 17 12 9 20 569 31 0 1 3 6 16 266 31 20 7 5 9 15
8 0 0 288 0 0 0 0 0 0 0 0 0 0 0 352 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
9 247 212 0 274 75 48 67 247 0 0 0 95 19 43 134 213 0 41 26 6 32 0 0 0 0 0 18 38 0 0 0 0 18 44 44
10 210 192 255 0 255 192 210 114 152 0 0 0 152 114 40 40 92 0 92 40 40 40 0 0 0 0 0 40 40 22 0 0 0 22 40
11 67 48 75 274 0 212 247 43 19 95 0 0 0 247 32 6 26 41 0 213 134 38 18 0 0 0 0 0 44 44 18 0 0 0 0
12 0 0 0 0 288 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 352 0 0 0 0 0 0 0 0 0 0 0 0 0 0
13 40 36 31 0 0 607 0 28 18 19 0 0 0 0 20 9 12 17 43 284 0 16 6 3 1 0 31 569 15 9 5 7 20 31 266
14 586 184 0 0 0 0 0 0 536 0 0 0 0 0 0 0 0 0 0 0 0 0 536 0 0 0 0 0 586 184 0 0 0 0 0
15 62 62 32 0 0 0 0 210 0 111 0 0 0 0 0 0 0 0 0 0 0 210 0 111 0 0 0 0 62 62 32 0 0 0 0
16 200 232 128 76 72 132 172 248 134 0 80 40 64 136 296 0 0 0 64 48 120 248 134 0 80 40 64 136 200 232 128 76 72 132 172
17 263 193 186 130 186 193 263 197 123 99 0 99 123 197 184 132 0 0 0 132 184 197 123 99 0 99 123 197 263 193 186 130 186 193 263
18 172 132 72 76 128 232 200 136 64 40 80 0 134 248 120 48 64 0 0 0 296 136 64 40 80 0 134 248 172 132 72 76 128 232 200
19 0 0 0 0 32 62 62 0 0 0 0 111 0 210 0 0 0 0 0 0 0 0 0 0 0 111 0 210 0 0 0 0 32 62 62
20 0 0 0 0 0 184 586 0 0 0 0 0 536 0 0 0 0 0 0 0 0 0 0 0 0 0 536 0 0 0 0 0 0 184 586
21 266 31 20 7 5 9 15 569 31 0 1 3 6 16 0 284 43 17 12 9 20 0 0 0 0 19 18 28 0 607 0 0 31 36 40
22 0 0 0 0 0 0 0 0 0 0 0 0 0 0 352 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 288 0 0 0 0
23 0 0 0 0 18 44 44 0 0 0 0 0 18 38 134 213 0 41 26 6 32 247 0 0 0 95 19 43 247 212 0 274 75 48 67
24 40 22 0 0 0 22 40 40 0 0 0 0 0 40 40 40 92 0 92 40 40 114 152 0 0 0 152 114 210 192 255 0 255 192 210
25 44 44 18 0 0 0 0 38 18 0 0 0 0 0 32 6 26 41 0 213 134 43 19 95 0 0 0 247 67 48 75 274 0 212 247
26 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 352 0 0 0 0 0 0 0 0 0 0 0 288 0 0
27 15 9 5 7 20 31 266 16 6 3 1 0 31 569 20 9 12 17 43 284 0 28 18 19 0 0 0 0 40 36 31 0 0 607 0
28 669 454 307 269 322 410 466 670 318 187 140 152 219 378 792 107 109 237 207 184 371 0 2 225 396 352 289 446 0 0 833 697 653 559 607
29 49 49 49 98 171 165 166 0 0 0 33 86 90 115 0 0 120 88 53 45 88 607 0 291 232 3 29 75 0 0 0 658 45 57 60
30 26 26 26 52 143 202 174 13 0 0 0 42 102 134 0 0 52 145 40 40 114 225 513 0 396 166 20 114 594 0 0 0 752 134 154
31 84 91 42 20 42 91 84 84 31 0 0 0 31 84 82 0 70 68 70 0 82 82 78 414 0 414 78 82 339 644 0 0 0 644 339
32 174 202 143 52 26 26 26 134 102 42 0 0 0 13 114 40 40 145 52 0 0 114 20 166 396 0 513 225 154 134 752 0 0 0 594
33 166 165 171 98 49 49 49 115 90 86 33 0 0 0 88 45 53 88 120 0 0 75 29 3 232 291 0 607 60 57 45 658 0 0 0
34 466 410 322 269 307 454 669 378 219 152 140 187 318 670 371 184 207 237 109 107 792 446 289 352 396 225 2 0 607 559 653 697 833 0 0
Sum of all rows = 4(3*0 + 1*2 + 1*107 + 1*109 + 1*140 + 1*152 + 1*184 + 1*187 + 1*207 + 1*219 + 1*225 + 1*237 + 1*269 + 1*289 + 1*307 + 1*318 + 1*322 + 1*352 + 1*371 + 1*378 + 1*396 + 1*410 + 1*446 + 1*454 +
1*466 + 1*559 + 1*607 + 1*653 + 1*669 + 1*670 + 1*697 + 1*792 + 1*833) +
4(9*0 + 1*3 + 1*29 + 1*33 + 2*45 + 3*49 + 1*53 + 1*57 + 1*60 + 1*75 + 1*86 + 2*88 + 1*90 + 1*98 + 1*115 + 1*120 + 1*165 + 1*166 + 1*171 + 1*232 + 1*291 + 1*607 + 1*658) +
4(9*0 + 1*13 + 1*20 + 3*26 + 2*40 + 1*42 + 2*52 + 1*102 + 2*114 + 2*134 + 1*143 + 1*145 + 1*154 + 1*166 + 1*174 + 1*202 + 1*225 + 1*396 + 1*513 + 1*594 + 1*752) +
2(9*0 + 1*20 + 2*31 + 2*42 + 1*68 + 2*70 + 2*78 + 4*82 + 4*84 + 2*91 + 2*339 + 2*414 + 2*644) +
4(9*0 + 1*1 + 1*3 + 1*5 + 1*6 + 1*7 + 2*9 + 1*12 + 1*15 + 1*16 + 1*17 + 1*18 + 1*19 + 2*20 + 1*28 + 3*31 + 1*36 + 1*40 + 1*43 + 1*266 + 1*284 + 1*569 + 1*607) +
4(33*0 + 1*288 + 1*352) +
4(14*0 + 1*6 + 2*18 + 1*19 + 1*26 + 1*32 + 1*38 + 1*41 + 1*43 + 2*44 + 1*48 + 1*67 + 1*75 + 1*95 + 1*134 + 1*212 + 1*213 + 2*247 + 1*274) +
2(13*0 + 2*22 + 8*40 + 2*92 + 2*114 + 2*152 + 2*192 + 2*210 + 2*255) +
2(29*0 + 2*184 + 2*536 + 2*586) +
2(25*0 + 2*32 + 4*62 + 2*111 + 2*210) +
2(5*0 + 2*40 + 1*48 + 3*64 + 2*72 + 2*76 + 2*80 + 1*120 + 2*128 + 2*132 + 2*134 + 2*136 + 2*172 + 2*200 + 2*232 + 2*248 + 1*296) +
1(5*0 + 4*99 + 4*123 + 2*130 + 2*132 + 2*184 + 4*186 + 4*193 + 4*197 + 4*263)
= 48108 + 14088 + 17596 + 8340 + 8572 + 2560 + 7764 + 4788 + 5224 + 1908 + 7912 + 5136
= 131996
Value repetition frequencies = 4(32*1 + 1*3) +
4(19*1 + 2*2 + 1*3 + 1*9) +
4(15*1 + 4*2 + 1*3 + 1*9) +
2(2*1 + 8*2 + 2*4 + 1*9) +
4(19*1 + 2*2 + 1*3 + 1*9) +
4(2*1 + 1*33) +
4(15*1 + 3*2 + 1*14) +
2(7*2 + 1*8 + 1*13) +
2(3*2 + 1*29) +
2(3*2 + 1*4 + 1*20) +
2(3*1 + 12*2 + 1*3 + 1*5) +
1(3*2 + 6*4 + 1*5)
= 1225
Number of distinct row element sets = 12
Number of rows = 1*1 + 5*2 + 6*4
= 35
Number of distinct values = 137
Distinct values 0 1 2 3 5 6 7 9 12 13 15 16 17 18 19 20 22 26 28 29 31 32 33 36 38
Frequency 475 4 4 8 4 8 4 8 4 4 4 4 4 12 8 14 4 16 4 4 16 8 4 4 4
Distinct values 40 41 42 43 44 45 48 49 52 53 57 60 62 64 67 68 70 72 75 76 78 80 82 84 86
Frequency 32 4 8 8 8 8 6 12 8 4 4 4 8 6 4 2 4 4 8 4 4 4 8 8 4
Distinct values 88 90 91 92 95 98 99 102 107 109 111 114 115 120 123 128 130 132 134 136 140 143 145 152 154
Frequency 8 4 4 4 4 4 4 4 4 4 4 12 4 6 4 4 2 6 16 4 4 4 4 8 4
Distinct values 165 166 171 172 174 184 186 187 192 193 197 200 202 207 210 212 213 219 225 232 237 247 248 255 263
Frequency 4 8 4 4 4 10 4 4 4 4 4 4 4 4 8 4 4 4 8 8 4 8 4 4 4
Distinct values 266 269 274 284 288 289 291 296 307 318 322 339 352 371 378 396 410 414 446 454 466 513 536 559 569
Frequency 4 4 4 4 4 4 4 2 4 4 4 4 8 4 4 8 4 4 4 4 4 4 4 4 4
Distinct values 586 594 607 644 653 658 669 670 697 752 792 833
Frequency 4 4 12 4 4 4 4 4 4 4 4 4
Sum of distinct value frequencies = 3*2 + 96*4 + 4*6 + 23*8 + 1*10 + 4*12 + 1*14 + 3*16 + 1*32 + 1*475
= 1225
Number of SN-EN pairs for which the number of CNSAPs is greater than zero = 4*2 + 2*6 + 2*10 + 4*21 + 2*22 + 14*26 + 3*30 + 4*32
= 750
Number of SN-EN pairs, with SN != EN, for which the number of CNSAPs equals zero = 440
Number of possible SN-EN pairs with SN != EN = 34*35
= 1190
a = 8, b = 5
L C S
3 8 2
4 16 4
5 40 10
6 88 22
7 220 50
8 360 104
9 776 238
10 1260 510
11 2792 982
12 3900 1628
13 7768 2496
14 9312 3724
15 19496 5774
16 19828 7514
17 40168 12958
18 35252 13418
19 68528 25184
20 50256 21404
21 87008 39668
22 46428 21634
23 60112 29588
24 26008 12984
25 17852 8926
26 2764 1382
27 64 32
Total 500304 210236
Number of times each node is the start node (SN) in a CNSAP of each length (L)
SN 0 1 2 3 4 5 6 7
8 9 10 11 12 13 14 15
16 17 18 19 20 21 22 23
24 25 26 27 28 29 30 31
32 33 34 35 36 37 38 39
L
3 0 0 0 0 0 0 0 0
0 2 0 0 0 0 2 0
0 0 0 0 0 0 0 0
0 2 0 0 0 0 2 0
0 0 0 0 0 0 0 0
4 0 0 0 0 0 0 0 0
0 0 2 0 0 2 0 0
0 4 0 0 0 0 4 0
0 0 2 0 0 2 0 0
0 0 0 0 0 0 0 0
5 0 0 1 0 0 1 0 0
0 2 0 2 2 0 2 0
2 0 8 0 0 8 0 2
0 2 0 2 2 0 2 0
0 0 1 0 0 1 0 0
6 0 2 0 3 3 0 2 0
3 0 6 2 2 6 0 3
0 0 0 12 12 0 0 0
3 0 6 2 2 6 0 3
0 2 0 3 3 0 2 0
7 5 1 9 5 5 9 1 5
1 4 4 16 16 4 4 1
2 2 0 16 16 0 2 2
1 4 4 16 16 4 4 1
5 1 9 5 5 9 1 5
8 0 8 7 23 23 7 8 0
4 4 3 29 29 3 4 4
0 0 20 4 4 20 0 0
4 4 3 29 29 3 4 4
0 8 7 23 23 7 8 0
9 13 14 14 53 53 14 14 13
7 7 50 11 11 50 7 7
6 26 0 18 18 0 26 6
7 7 50 11 11 50 7 7
13 14 14 53 53 14 14 13
10 17 16 95 21 21 95 16 17
10 75 6 27 27 6 75 10
30 2 56 8 8 56 2 30
10 75 6 27 27 6 75 10
17 16 95 21 21 95 16 17
11 33 177 39 54 54 39 177 33
122 31 97 39 39 97 31 122
26 138 8 40 40 8 138 26
122 31 97 39 39 97 31 122
33 177 39 54 54 39 177 33
12 267 39 95 50 50 95 39 267
32 214 24 52 52 24 214 32
254 14 116 20 20 116 14 254
32 214 24 52 52 24 214 32
267 39 95 50 50 95 39 267
13 85 297 136 189 189 136 297 85
515 110 190 122 122 190 110 515
110 362 40 84 84 40 362 110
515 110 190 122 122 190 110 515
85 297 136 189 189 136 297 85
14 550 107 284 153 153 284 107 550
122 378 87 113 113 87 378 122
792 82 162 32 32 162 82 792
122 378 87 113 113 87 378 122
550 107 284 153 153 284 107 550
15 267 829 448 626 626 448 829 267
991 346 451 304 304 451 346 991
396 520 162 146 146 162 520 396
991 346 451 304 304 451 346 991
267 829 448 626 626 448 829 267
16 1255 350 740 406 406 740 350 1255
415 638 235 260 260 235 638 415
712 288 250 66 66 250 288 712
415 638 235 260 260 235 638 415
1255 350 740 406 406 740 350 1255
17 818 1621 1113 1549 1549 1113 1621 818
1265 904 909 611 611 909 904 1265
1098 840 350 216 216 350 840 1098
1265 904 909 611 611 909 904 1265
818 1621 1113 1549 1549 1113 1621 818
18 1483 913 1307 925 925 1307 913 1483
1163 780 414 642 642 414 780 1163
1256 542 324 250 250 324 542 1256
1163 780 414 642 642 414 780 1163
1483 913 1307 925 925 1307 913 1483
19 2031 1974 1936 2770 2770 1936 1974 2031
2301 1689 965 1160 1160 965 1689 2301
2342 1386 342 542 542 342 1386 2342
2301 1689 965 1160 1160 965 1689 2301
2031 1974 1936 2770 2770 1936 1974 2031
20 2296 1513 958 1510 1510 958 1513 2296
2171 621 695 1100 1100 695 621 2171
1870 290 490 750 750 490 290 1870
2171 621 695 1100 1100 695 621 2171
2296 1513 958 1510 1510 958 1513 2296
21 3378 2519 2865 2294 2294 2865 2519 3378
2946 1911 1115 1602 1602 1115 1911 2946
3384 1194 450 1216 1216 450 1194 3384
2946 1911 1115 1602 1602 1115 1911 2946
3378 2519 2865 2294 2294 2865 2519 3378
22 2207 2012 1253 795 795 1253 2012 2207
1726 577 626 838 838 626 577 1726
504 344 822 1476 1476 822 344 504
1726 577 626 838 838 626 577 1726
2207 2012 1253 795 795 1253 2012 2207
23 2740 2429 1848 1292 1292 1848 2429 2740
1396 962 1112 1121 1121 1112 962 1396
1882 432 578 1364 1364 578 432 1882
1396 962 1112 1121 1121 1112 962 1396
2740 2429 1848 1292 1292 1848 2429 2740
24 1015 1265 1125 534 534 1125 1265 1015
575 102 284 252 252 284 102 575
112 194 848 1546 1546 848 194 112
575 102 284 252 252 284 102 575
1015 1265 1125 534 534 1125 1265 1015
25 639 600 781 493 493 781 600 639
356 87 374 271 271 374 87 356
468 38 560 658 658 560 38 468
356 87 374 271 271 374 87 356
639 600 781 493 493 781 600 639
26 184 42 59 133 133 59 42 184
10 0 48 38 38 48 0 10
0 60 262 32 32 262 60 0
10 0 48 38 38 48 0 10
184 42 59 133 133 59 42 184
27 4 7 0 0 0 0 7 4
0 0 0 0 0 0 0 0
0 0 10 0 0 10 0 0
0 0 0 0 0 0 0 0
4 7 0 0 0 0 7 4
Total 19287 16735 15113 13878 13878 15113 16735 19287
16131 9444 7697 8612 8612 7697 9444 16131
15246 6758 5858 8496 8496 5858 6758 15246
16131 9444 7697 8612 8612 7697 9444 16131
19287 16735 15113 13878 13878 15113 16735 19287
Grand total = 2*5858 + 2*6758 + 4*7697 + 2*8496 + 4*8612 + 4*9444 + 4*13878 + 4*15113 + 2*15246 + 4*16131 + 4*16735 + 4*19287
= 500304
Number of times each node is the end node (EN) in a CNSAP of each length (L)
EN 0 1 2 3 4 5 6 7
8 9 10 11 12 13 14 15
16 17 18 19 20 21 22 23
24 25 26 27 28 29 30 31
32 33 34 35 36 37 38 39
L
3 2 0 0 0 0 0 0 2
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
2 0 0 0 0 0 0 2
4 4 0 0 0 0 0 0 4
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
4 0 0 0 0 0 0 4
5 10 0 0 0 0 0 0 10
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
10 0 0 0 0 0 0 10
6 22 0 0 0 0 0 0 22
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
22 0 0 0 0 0 0 22
7 46 2 2 2 2 2 2 46
2 0 0 0 0 0 0 2
2 0 0 0 0 0 0 2
2 0 0 0 0 0 0 2
46 2 2 2 2 2 2 46
8 83 1 2 2 2 2 1 83
1 0 0 0 0 0 0 1
2 0 0 0 0 0 0 2
1 0 0 0 0 0 0 1
83 1 2 2 2 2 1 83
9 159 6 9 10 10 9 6 159
6 0 0 0 0 0 0 6
8 0 0 0 0 0 0 8
6 0 0 0 0 0 0 6
159 6 9 10 10 9 6 159
10 280 6 9 13 13 9 6 280
5 0 0 0 0 0 0 5
4 0 0 0 0 0 0 4
5 0 0 0 0 0 0 5
280 6 9 13 13 9 6 280
11 505 26 44 48 48 44 26 505
19 4 8 8 8 8 4 19
32 8 16 16 16 16 8 32
19 4 8 8 8 8 4 19
505 26 44 48 48 44 26 505
12 815 26 42 49 49 42 26 815
11 0 4 4 4 4 0 11
12 4 16 16 16 16 4 12
11 0 4 4 4 4 0 11
815 26 42 49 49 42 26 815
13 1164 99 164 191 191 164 99 1164
60 20 44 56 56 44 20 60
88 32 72 96 96 72 32 88
60 20 44 56 56 44 20 60
1164 99 164 191 191 164 99 1164
14 1718 87 140 159 159 140 87 1718
20 0 32 46 46 32 0 20
24 16 88 124 124 88 16 24
20 0 32 46 46 32 0 20
1718 87 140 159 159 140 87 1718
15 2261 297 500 653 653 500 297 2261
175 72 174 276 276 174 72 175
232 84 240 376 376 240 84 232
175 72 174 276 276 174 72 175
2261 297 500 653 653 500 297 2261
16 2970 219 381 488 488 381 219 2970
62 0 139 240 240 139 0 62
44 30 314 528 528 314 30 44
62 0 139 240 240 139 0 62
2970 219 381 488 488 381 219 2970
17 3457 698 1203 1575 1575 1203 698 3457
439 177 480 776 776 480 177 439
548 196 682 1048 1048 682 196 548
439 177 480 776 776 480 177 439
3457 698 1203 1575 1575 1203 698 3457
18 3963 499 860 1112 1112 860 499 3963
182 0 332 716 716 332 0 182
104 42 758 1394 1394 758 42 104
182 0 332 716 716 332 0 182
3963 499 860 1112 1112 860 499 3963
19 4791 1432 2344 2457 2457 2344 1432 4791
930 357 948 1376 1376 948 357 930
1198 414 1346 2036 2036 1346 414 1198
930 357 948 1376 1376 948 357 930
4791 1432 2344 2457 2457 2344 1432 4791
20 4519 908 1521 1527 1527 1521 908 4519
325 0 578 1157 1157 578 0 325
270 76 1332 2380 2380 1332 76 270
325 0 578 1157 1157 578 0 325
4519 908 1521 1527 1527 1521 908 4519
21 5116 2487 2964 2467 2467 2964 2487 5116
1678 640 1120 1458 1458 1120 640 1678
2312 812 1828 2692 2692 1828 812 2312
1678 640 1120 1458 1458 1120 640 1678
5116 2487 2964 2467 2467 2964 2487 5116
22 3265 1261 1524 1294 1294 1524 1261 3265
553 0 659 625 625 659 0 553
512 166 1784 2390 2390 1784 166 512
553 0 659 625 625 659 0 553
3265 1261 1524 1294 1294 1524 1261 3265
23 3038 1976 2173 1687 1687 2173 1976 3038
1189 334 913 868 868 913 334 1189
1580 544 1746 1830 1830 1746 544 1580
1189 334 913 868 868 913 334 1189
3038 1976 2173 1687 1687 2173 1976 3038
24 1344 797 1026 784 784 1026 797 1344
384 0 345 282 282 345 0 384
168 196 1500 1216 1216 1500 196 168
384 0 345 282 282 345 0 384
1344 797 1026 784 784 1026 797 1344
25 772 478 675 588 588 675 478 772
296 85 341 288 288 341 85 296
404 94 820 562 562 820 94 404
296 85 341 288 288 341 85 296
772 478 675 588 588 675 478 772
26 181 47 59 133 133 59 47 181
8 0 48 38 38 48 0 8
0 58 272 24 24 272 58 0
8 0 48 38 38 48 0 8
181 47 59 133 133 59 47 181
27 4 7 0 0 0 0 7 4
0 0 0 0 0 0 0 0
0 0 10 0 0 10 0 0
0 0 0 0 0 0 0 0
4 7 0 0 0 0 7 4
Total 40489 11359 15642 15239 15239 15642 11359 40489
6345 1689 6165 8214 8214 6165 1689 6345
7544 2772 12824 16728 16728 12824 2772 7544
6345 1689 6165 8214 8214 6165 1689 6345
40489 11359 15642 15239 15239 15642 11359 40489
Grand total = 4*1689 + 2*2772 + 4*6165 + 4*6345 + 2*7544 + 4*8214 + 4*11359 + 2*12824 + 4*15239 + 4*15642 + 2*16728 + 4*40489
= 500304
Number of times each node (N) is present in a CNSAP of each length (L)
N 0 1 2 3 4 5 6 7
8 9 10 11 12 13 14 15
16 17 18 19 20 21 22 23
24 25 26 27 28 29 30 31
32 33 34 35 36 37 38 39
L
3 2 1 0 0 0 0 1 2
1 2 0 0 0 0 2 1
0 0 0 0 0 0 0 0
1 2 0 0 0 0 2 1
2 1 0 0 0 0 1 2
4 4 2 0 0 0 0 2 4
2 4 2 0 0 2 4 2
0 4 0 0 0 0 4 0
2 4 2 0 0 2 4 2
4 2 0 0 0 0 2 4
5 10 5 1 0 0 1 5 10
5 12 5 2 2 5 12 5
2 10 8 0 0 8 10 2
5 12 5 2 2 5 12 5
10 5 1 0 0 1 5 10
6 22 13 1 3 3 1 13 22
14 28 17 8 8 17 28 14
2 22 16 12 12 16 22 2
14 28 17 8 8 17 28 14
22 13 1 3 3 1 13 22
7 53 32 17 12 12 17 32 53
31 60 49 36 36 49 60 31
14 58 62 56 56 62 58 14
31 60 49 36 36 49 60 31
53 32 17 12 12 17 32 53
8 86 54 27 37 37 27 54 86
50 103 93 101 101 93 103 50
10 78 126 124 124 126 78 10
50 103 93 101 101 93 103 50
86 54 27 37 37 27 54 86
9 183 122 71 128 128 71 122 183
115 212 241 241 241 241 212 115
44 190 292 340 340 292 190 44
115 212 241 241 241 241 212 115
183 122 71 128 128 71 122 183
10 317 204 186 199 199 186 204 317
181 425 419 452 452 419 425 181
62 330 526 616 616 526 330 62
181 425 419 452 452 419 425 181
317 204 186 199 199 186 204 317
11 606 595 459 513 513 459 595 606
526 955 1056 1106 1106 1056 955 526
268 878 1148 1430 1430 1148 878 268
526 955 1056 1106 1106 1056 955 526
606 595 459 513 513 459 595 606
12 1160 856 677 785 785 677 856 1160
722 1623 1531 1575 1575 1531 1623 722
456 1396 1808 1882 1882 1808 1396 456
722 1623 1531 1575 1575 1531 1623 722
1160 856 677 785 785 677 856 1160
13 1695 1909 1972 2405 2405 1972 1909 1695
1854 3001 3209 3607 3607 3209 3001 1854
1310 3068 3268 3542 3542 3268 3068 1310
1854 3001 3209 3607 3607 3209 3001 1854
1695 1909 1972 2405 2405 1972 1909 1695
14 2701 2356 2481 2988 2988 2481 2356 2701
2260 4366 4129 4017 4017 4129 4366 2260
2008 4332 4412 3836 3836 4412 4332 2008
2260 4366 4129 4017 4017 4129 4366 2260
2701 2356 2481 2988 2988 2481 2356 2701
15 4196 5846 7233 9043 9043 7233 5846 4196
5368 8229 8792 9192 9192 8792 8229 5368
5180 8600 8492 8150 8150 8492 8600 5180
5368 8229 8792 9192 9192 8792 8229 5368
4196 5846 7233 9043 9043 7233 5846 4196
16 5959 6497 7578 8730 8730 7578 6497 5959
6151 10005 9321 8676 8676 9321 10005 6151
5740 10032 9308 7710 7710 9308 10032 5740
6151 10005 9321 8676 8676 9321 10005 6151
5959 6497 7578 8730 8730 7578 6497 5959
17 9443 14725 19588 22591 22591 19588 14725 9443
13275 19154 20677 18172 18172 20677 19154 13275
14492 19574 18756 13356 13356 18756 19574 14492
13275 19154 20677 18172 18172 20677 19154 13275
9443 14725 19588 22591 22591 19588 14725 9443
18 10803 14767 17262 18971 18971 17262 14767 10803
13856 18786 17087 16256 16256 17087 18786 13856
14518 18658 15558 12958 12958 15558 18658 14518
13856 18786 17087 16256 16256 17087 18786 13856
10803 14767 17262 18971 18971 17262 14767 10803
19 19015 31637 39311 43912 43912 39311 31637 19015
29289 39399 32398 30888 30888 32398 39399 29289
33878 40990 25010 19440 19440 25010 40990 33878
29289 39399 32398 30888 30888 32398 39399 29289
19015 31637 39311 43912 43912 39311 31637 19015
20 18027 25379 29147 32241 32241 29147 25379 18027
25895 27804 23264 23506 23506 23264 27804 25895
28678 27196 18768 17392 17392 18768 27196 28678
25895 27804 23264 23506 23506 23264 27804 25895
18027 25379 29147 32241 32241 29147 25379 18027
21 32725 46922 56639 59802 59802 56639 46922 32725
54920 46806 40003 40125 40125 40003 46806 54920
66790 43436 24972 22502 22502 24972 43436 66790
54920 46806 40003 40125 40125 40003 46806 54920
32725 46922 56639 59802 59802 56639 46922 32725
22 20416 28361 31436 31280 31280 31436 28361 20416
31769 24998 20767 21557 21557 20767 24998 31769
36132 21296 14244 17868 17868 14244 21296 36132
31769 24998 20767 21557 21557 20767 24998 31769
20416 28361 31436 31280 31280 31436 28361 20416
23 29672 40931 44629 38007 38007 44629 40931 29672
45422 29688 29533 31709 31709 29533 29688 45422
54264 22882 14756 20204 20204 14756 22882 54264
45422 29688 29533 31709 31709 29533 29688 45422
29672 40931 44629 38007 38007 44629 40931 29672
24 14575 19993 20686 16946 16946 20686 19993 14575
20836 11832 10885 12229 12229 10885 11832 20836
23994 9854 8672 13612 13612 8672 9854 23994
20836 11832 10885 12229 12229 10885 11832 20836
14575 19993 20686 16946 16946 20686 19993 14575
25 11213 15577 16303 10610 10610 16303 15577 11213
14871 6685 7974 8088 8088 7974 6685 14871
17298 5066 6596 11548 11548 6596 5066 17298
14871 6685 7974 8088 8088 7974 6685 14871
11213 15577 16303 10610 10610 16303 15577 11213
26 2054 2543 2604 1604 1604 2604 2543 2054
2360 784 1314 1344 1344 1314 784 2360
2732 808 1434 1744 1744 1434 808 2732
2360 784 1314 1344 1344 1314 784 2360
2054 2543 2604 1604 1604 2604 2543 2054
27 54 60 50 46 46 50 60 54
60 10 36 36 36 36 10 60
64 8 60 28 28 60 8 64
60 10 36 36 36 36 10 60
54 60 50 46 46 50 60 54
Total 184991 259387 298358 300853 300853 298358 259387 184991
269833 254971 232802 232923 232923 232802 254971 269833
307936 238766 178292 178350 178350 178292 238766 307936
269833 254971 232802 232923 232923 232802 254971 269833
184991 259387 298358 300853 300853 298358 259387 184991
Grand total = 2*178292 + 2*178350 + 4*184991 + 4*232802 + 4*232923 + 2*238766 + 4*254971 + 4*259387 + 4*269833 + 4*298358 + 4*300853 + 2*307936
= 9943160
Number of CNSAPs for each start node (SN) and end node (EN) pair
SN 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
EN
0 0 0 2328 1901 1758 1505 1458 1651 0 2 563 1215 1176 817 755 1264 2291 297 255 735 830 618 555 1134 1976 923 543 409 450 647 788 1258 1988 1375 915 742 908 1321 1504 1634
1 0 0 0 1762 69 116 128 208 1720 0 892 662 3 29 99 219 0 0 346 248 226 194 126 260 0 0 0 116 327 309 237 360 142 142 142 280 493 501 484 519
2 1723 0 0 0 1974 154 234 254 607 1374 0 1266 654 20 114 308 0 0 196 550 220 220 208 382 49 0 0 0 198 494 416 516 98 98 98 196 571 908 778 764
3 947 1733 0 0 0 1830 397 477 251 225 1063 0 1150 405 90 353 251 0 198 307 423 88 162 387 264 112 0 0 0 205 387 463 264 313 175 103 246 618 735 617
4 477 397 1830 0 0 0 1733 947 353 90 405 1150 0 1063 225 251 387 162 88 423 307 198 0 251 463 387 205 0 0 0 112 264 617 735 618 246 103 175 313 264
5 254 234 154 1974 0 0 0 1723 308 114 20 654 1266 0 1374 607 382 208 220 220 550 196 0 0 516 416 494 198 0 0 0 49 764 778 908 571 196 98 98 98
6 208 128 116 69 1762 0 0 0 219 99 29 3 662 892 0 1720 260 126 194 226 248 346 0 0 360 237 309 327 116 0 0 0 519 484 501 493 280 142 142 142
7 1651 1458 1505 1758 1901 2328 0 0 1264 755 817 1176 1215 563 2 0 1134 555 618 830 735 255 297 2291 1258 788 647 450 409 543 923 1976 1634 1504 1321 908 742 915 1375 1988
8 0 1720 0 0 73 89 89 103 0 0 0 0 60 50 45 74 0 792 105 43 48 27 28 59 1605 101 0 1 3 6 32 57 782 101 70 21 8 27 59 67
9 0 0 767 0 0 0 0 0 0 0 0 0 0 0 0 0 922 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
10 668 667 0 692 162 83 102 115 668 0 0 0 312 19 55 103 352 564 0 156 116 26 58 118 0 0 0 0 0 90 128 150 0 0 0 0 87 230 230 214
11 703 644 828 0 731 398 272 386 381 510 0 0 0 474 114 250 134 134 292 0 222 128 40 188 134 0 0 0 0 0 120 228 134 81 0 0 0 132 288 268
12 386 272 398 731 0 828 644 703 250 114 474 0 0 0 510 381 188 40 128 222 0 292 134 134 228 120 0 0 0 0 0 134 268 288 132 0 0 0 81 134
13 115 102 83 162 692 0 667 668 103 55 19 312 0 0 0 668 118 58 26 116 156 0 564 352 150 128 90 0 0 0 0 0 214 230 230 87 0 0 0 0
14 0 0 0 0 0 767 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 922 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
15 103 89 89 73 0 0 1720 0 74 45 50 60 0 0 0 0 59 28 27 48 43 105 792 0 57 32 6 3 1 0 101 1605 67 59 27 8 21 70 101 782
16 1710 570 0 0 0 0 0 0 0 1492 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1492 0 0 0 0 0 0 1710 570 0 0 0 0 0 0
17 190 190 104 0 0 0 0 0 586 0 316 0 0 0 0 0 0 0 0 0 0 0 0 0 586 0 316 0 0 0 0 0 190 190 104 0 0 0 0 0
18 544 684 400 204 148 336 472 528 692 410 0 226 96 140 248 408 840 0 0 0 248 120 176 368 692 410 0 226 96 140 248 408 544 684 400 204 148 336 472 528
19 796 596 678 377 372 360 591 793 574 396 404 0 288 211 271 613 548 444 0 0 0 352 210 534 574 396 404 0 288 211 271 613 796 596 678 377 372 360 591 793
20 793 591 360 372 377 678 596 796 613 271 211 288 0 404 396 574 534 210 352 0 0 0 444 548 613 271 211 288 0 404 396 574 793 591 360 372 377 678 596 796
21 528 472 336 148 204 400 684 544 408 248 140 96 226 0 410 692 368 176 120 248 0 0 0 840 408 248 140 96 226 0 410 692 528 472 336 148 204 400 684 544
22 0 0 0 0 0 104 190 190 0 0 0 0 0 316 0 586 0 0 0 0 0 0 0 0 0 0 0 0 0 316 0 586 0 0 0 0 0 104 190 190
23 0 0 0 0 0 0 570 1710 0 0 0 0 0 0 1492 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1492 0 0 0 0 0 0 0 570 1710
24 782 101 70 21 8 27 59 67 1605 101 0 1 3 6 32 57 0 792 105 43 48 27 28 59 0 0 0 0 60 50 45 74 0 1720 0 0 73 89 89 103
25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 922 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 767 0 0 0 0 0
26 0 0 0 0 87 230 230 214 0 0 0 0 0 90 128 150 352 564 0 156 116 26 58 118 668 0 0 0 312 19 55 103 668 667 0 692 162 83 102 115
27 134 81 0 0 0 132 288 268 134 0 0 0 0 0 120 228 134 134 292 0 222 128 40 188 381 510 0 0 0 474 114 250 703 644 828 0 731 398 272 386
28 268 288 132 0 0 0 81 134 228 120 0 0 0 0 0 134 188 40 128 222 0 292 134 134 250 114 474 0 0 0 510 381 386 272 398 731 0 828 644 703
29 214 230 230 87 0 0 0 0 150 128 90 0 0 0 0 0 118 58 26 116 156 0 564 352 103 55 19 312 0 0 0 668 115 102 83 162 692 0 667 668
30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 922 0 0 0 0 0 0 0 0 0 0 0 0 0 767 0 0
31 67 59 27 8 21 70 101 782 57 32 6 3 1 0 101 1605 59 28 27 48 43 105 792 0 74 45 50 60 0 0 0 0 103 89 89 73 0 0 1720 0
32 1988 1375 915 742 908 1321 1504 1634 1976 923 543 409 450 647 788 1258 2291 297 255 735 830 618 555 1134 0 2 563 1215 1176 817 755 1264 0 0 2328 1901 1758 1505 1458 1651
33 142 142 142 280 493 501 484 519 0 0 0 116 327 309 237 360 0 0 346 248 226 194 126 260 1720 0 892 662 3 29 99 219 0 0 0 1762 69 116 128 208
34 98 98 98 196 571 908 778 764 49 0 0 0 198 494 416 516 0 0 196 550 220 220 208 382 607 1374 0 1266 654 20 114 308 1723 0 0 0 1974 154 234 254
35 264 313 175 103 246 618 735 617 264 112 0 0 0 205 387 463 251 0 198 307 423 88 162 387 251 225 1063 0 1150 405 90 353 947 1733 0 0 0 1830 397 477
36 617 735 618 246 103 175 313 264 463 387 205 0 0 0 112 264 387 162 88 423 307 198 0 251 353 90 405 1150 0 1063 225 251 477 397 1830 0 0 0 1733 947
37 764 778 908 571 196 98 98 98 516 416 494 198 0 0 0 49 382 208 220 220 550 196 0 0 308 114 20 654 1266 0 1374 607 254 234 154 1974 0 0 0 1723
38 519 484 501 493 280 142 142 142 360 237 309 327 116 0 0 0 260 126 194 226 248 346 0 0 219 99 29 3 662 892 0 1720 208 128 116 69 1762 0 0 0
39 1634 1504 1321 908 742 915 1375 1988 1258 788 647 450 409 543 923 1976 1134 555 618 830 735 255 297 2291 1264 755 817 1176 1215 563 2 0 1651 1458 1505 1758 1901 2328 0 0
Sum of all rows = 4(3*0 + 1*2 + 1*255 + 1*297 + 1*409 + 1*450 + 1*543 + 1*555 + 1*563 + 1*618 + 1*647 + 1*735 + 1*742 + 1*755 + 1*788 + 1*817 + 1*830 + 1*908 + 1*915 + 1*923 + 1*1134 + 1*1176 + 1*1215 + 1*1258 +
1*1264 + 1*1321 + 1*1375 + 1*1458 + 1*1504 + 1*1505 + 1*1634 + 1*1651 + 1*1758 + 1*1901 + 1*1976 + 1*1988 + 1*2291 + 1*2328) +
4(9*0 + 1*3 + 1*29 + 1*69 + 1*99 + 2*116 + 1*126 + 1*128 + 3*142 + 1*194 + 1*208 + 1*219 + 1*226 + 1*237 + 1*248 + 1*260 + 1*280 + 1*309 + 1*327 + 1*346 + 1*360 + 1*484 + 1*493 + 1*501 + 1*519 +
1*662 + 1*892 + 1*1720 + 1*1762) +
4(9*0 + 1*20 + 1*49 + 3*98 + 1*114 + 1*196 + 1*208 + 2*220 + 1*308 + 1*382 + 1*154 + 1*196 + 1*198 + 1*234 + 1*254 + 1*416 + 1*494 + 1*516 + 1*550 + 1*571 + 1*607 + 1*654 + 1*764 + 1*778 +
1*908 + 1*1266 + 1*1374 + 1*1723 + 1*1974) +
4(8*0 + 1*88 + 1*90 + 1*103 + 1*112 + 1*162 + 1*175 + 1*198 + 1*205 + 1*225 + 1*246 + 2*251 + 2*264 + 1*307 + 1*313 + 1*353 + 2*387 + 1*397 + 1*405 + 1*423 + 1*463 + 1*477 + 1*617 + 1*618 +
1*735 + 1*947 + 1*1063 + 1*1150 + 1*1733 + 1*1830) +
4(9*0 + 1*1 + 1*3 + 1*6 + 1*8 + 1*21 + 2*27 + 1*28 + 1*32 + 1*43 + 1*45 + 1*48 + 1*50 + 1*57 + 1*2 + 1*59 + 1*60 + 1*67 + 1*70 + 1*73 + 1*74 + 2*89 + 2*101 + 1*103 + 1*105 + 1*782 + 1*792 +
1*1605 + 1*1720) +
4(38*0 + 1*767 + 1*922) +
4(14*0 + 1*19 + 1*26 + 1*55 + 1*58 + 1*83 + 1*87 + 1*90 + 1*102 + 1*103 + 1*115 + 1*116 + 1*118 + 1*128 + 1*150 + 1*156 + 1*162 + 1*214 + 2*230 + 1*312 + 1*352 + 1*564 + 1*667 + 2*668 + 1*692) +
4(13*0 + 1*40 + 1*81 + 1*114 + 1*120 + 1*128 + 1*132 + 4*134 + 1*188 + 1*222 + 1*228 + 1*250 + 1*268 + 1*272 + 1*288 + 1*292 + 1*381 + 1*386 + 1*398 + 1*474 + 1*510 + 1*644 + 1*703 + 1*731 +
1*828) +
2(34*0 + 2*570 + 2*1492 + 2*1710) +
2(30*0 + 2*104 + 4*190 + 2*316 + 2*586) +
2(5*0 + 2*96 + 1*120 + 2*140 + 2*148 + 1*176 + 2*204 + 2*226 + 3*248 + 2*336 + 1*368 + 2*400 + 2*408 + 2*410 + 2*472 + 2*528 + 2*544 + 2*684 + 2*692 + 1*840) +
2(5*0 + 1*360 + 1*210 + 2*211 + 2*271 + 2*288 + 1*352 + 1*360 + 2*372 + 2*377 + 2*396 + 2*404 + 1*444 + 1*534 + 1*548 + 2*574 + 2*591 + 2*596 + 2*613 + 2*678 + 2*793 + 2*796)
= 161956 + 45436 + 62568 + 60956 + 25380 + 6756 + 24660 + 32856 + 15088 + 5544 + 25648 + 33456
= 500304
Value repetition frequencies = 4(37*1 + 1*3) +
4(26*1 + 1*2 + 1*3 + 1*9) +
4(26*1 + 1*2 + 1*3 + 1*9) +
4(26*1 + 3*2 + 1*8) +
4(25*1 + 3*2 + 1*9) +
4(2*1 + 1*38) +
4(22*1 + 2*2 + 1*14) +
4(23*1 + 1*4 + 1*13) +
2(3*2 + 1*34) +
2(3*2 + 1*4 + 1*30) +
2(4*1 + 14*2 + 1*3 + 1*5) +
2(7*1 + 14*2 + 1*5)
= 1600
Number of distinct row element sets = 12
Number of rows = 4*2 + 8*4
= 40
Number of distinct values = 223
Distinct values 0 1 2 3 6 8 19 20 21 26 27 28 29 32 40 43 45 48 49 50
Frequency 560 4 4 8 4 4 4 4 4 4 8 4 4 4 4 4 4 4 4 4
Distinct values 55 57 58 59 60 67 69 70 73 74 81 83 87 88 89 90 96 98 99 101
Frequency 4 4 4 8 4 4 4 4 4 4 4 4 4 4 8 8 4 12 4 8
Distinct values 102 103 104 105 112 114 115 116 118 120 126 128 132 134 140 142 148 150 154 156
Frequency 4 12 4 4 4 8 4 12 4 6 4 12 4 16 4 12 4 4 4 4
Distinct values 162 175 176 188 190 194 196 198 204 205 208 210 211 214 219 220 222 225 226 228
Frequency 8 4 2 4 8 4 8 8 4 4 8 2 4 4 4 8 4 4 8 4
Distinct values 230 234 237 246 248 250 251 254 255 260 264 268 271 272 280 288 292 297 307 308
Frequency 8 4 4 4 10 4 8 4 4 4 8 4 4 4 4 8 4 4 4 4
Distinct values 309 312 313 316 327 336 346 352 353 360 368 372 377 381 382 386 387 396 397 398
Frequency 4 4 4 4 4 4 4 6 4 8 2 4 4 4 4 4 8 4 4 4
Distinct values 400 404 405 408 409 410 416 423 444 450 463 472 474 477 484 493 494 501 510 516
Frequency 4 4 4 4 4 4 4 4 2 4 4 4 4 4 4 4 4 4 4 4
Distinct values 519 528 534 543 544 548 550 555 563 564 570 571 574 586 591 596 607 613 617 618
Frequency 4 4 2 4 4 2 4 4 4 4 4 4 4 4 4 4 4 4 4 8
Distinct values 644 647 654 662 667 668 678 684 692 703 731 735 742 755 764 767 778 782 788 792
Frequency 4 4 4 4 4 8 4 4 8 4 4 8 4 4 4 4 4 4 4 4
Distinct values 793 796 817 828 830 840 892 908 915 922 923 947 1063 1134 1150 1176 1215 1258 1264 1266
Frequency 4 4 4 4 4 2 4 8 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 1321 1374 1375 1458 1492 1504 1505 1605 1634 1651 1710 1720 1723 1733 1758 1762 1830 1901 1974 1976
Frequency 4 4 4 4 4 4 4 4 4 4 4 8 4 4 4 4 4 4 4 4
Distinct values 1988 2291 2328
Frequency 4 4 4
Sum of distinct value frequencies = 7*2 + 180*4 + 2*6 + 26*8 + 1*10 + 5*12 + 1*16 + 1*560
= 1600
Number of SN-EN pairs for which the number of CNSAPs is greater than zero = 4*2 + 2*6 + 2*10 + 4*26 + 4*27 + 12*31 + 4*32 + 4*35 + 4*37
= 1040
Number of SN-EN pairs, with SN != EN, for which the number of CNSAPs equals zero = 520
Number of possible SN-EN pairs with SN != EN = 39*40
= 1560
a = 9, b = 5
L C S
3 8 2
4 16 4
5 40 10
6 88 22
7 224 50
8 364 104
9 796 238
10 1296 514
11 3052 1040
12 4628 1906
13 10812 3650
14 13800 5542
15 30824 9888
16 33640 12692
17 69484 22392
18 67280 23762
19 129200 41730
20 121752 44704
21 211052 76292
22 171068 69700
23 276984 117034
24 170252 75466
25 261620 124404
26 121676 59834
27 125892 62922
28 31288 15644
29 4800 2400
30 216 108
Total 1862152 772054
Number of times each node is the start node (SN) in a CNSAP of each length (L)
SN 0 1 2 3 4 5 6 7 8
9 10 11 12 13 14 15 16 17
18 19 20 21 22 23 24 25 26
27 28 29 30 31 32 33 34 35
36 37 38 39 40 41 42 43 44
L
3 0 0 0 0 0 0 0 0 0
0 2 0 0 0 0 0 2 0
0 0 0 0 0 0 0 0 0
0 2 0 0 0 0 0 2 0
0 0 0 0 0 0 0 0 0
4 0 0 0 0 0 0 0 0 0
0 0 2 0 0 0 2 0 0
0 4 0 0 0 0 0 4 0
0 0 2 0 0 0 2 0 0
0 0 0 0 0 0 0 0 0
5 0 0 1 0 0 0 1 0 0
0 2 0 2 0 2 0 2 0
2 0 8 0 0 0 8 0 2
0 2 0 2 0 2 0 2 0
0 0 1 0 0 0 1 0 0
6 0 2 0 3 0 3 0 2 0
3 0 6 0 4 0 6 0 3
0 0 0 12 0 12 0 0 0
3 0 6 0 4 0 6 0 3
0 2 0 3 0 3 0 2 0
7 5 1 9 0 10 0 9 1 5
1 4 2 18 2 18 2 4 1
2 2 0 0 32 0 0 2 2
1 4 2 18 2 18 2 4 1
5 1 9 0 10 0 9 1 5
8 0 8 0 30 0 30 0 8 0
4 2 5 2 56 2 5 2 4
0 0 0 24 0 24 0 0 0
4 2 5 2 56 2 5 2 4
0 8 0 30 0 30 0 8 0
9 13 5 23 4 102 4 23 5 13
5 9 4 57 6 57 4 9 5
6 2 24 0 36 0 24 2 6
5 9 4 57 6 57 4 9 5
13 5 23 4 102 4 23 5 13
10 6 27 4 112 6 112 4 27 6
12 4 77 4 52 4 77 4 12
2 30 2 62 4 62 2 30 2
12 4 77 4 52 4 77 4 12
6 27 4 112 6 112 4 27 6
11 46 23 193 25 88 25 193 23 46
20 133 22 116 30 116 22 133 20
58 14 132 12 72 12 132 14 58
20 133 22 116 30 116 22 133 20
46 23 193 25 88 25 193 23 46
12 23 283 21 131 22 131 21 283 23
171 19 221 19 98 19 221 19 171
14 254 14 130 12 130 14 254 14
171 19 221 19 98 19 221 19 171
23 283 21 131 22 131 21 283 23
13 452 98 344 113 292 113 344 98 452
84 545 90 243 114 243 90 545 84
524 70 344 48 152 48 344 70 524
84 545 90 243 114 243 90 545 84
452 98 344 113 292 113 344 98 452
14 86 612 82 398 64 398 82 612 86
978 94 407 61 224 61 407 94 978
88 820 74 178 32 178 74 820 88
978 94 407 61 224 61 407 94 978
86 612 82 398 64 398 82 612 86
15 1353 340 1038 417 964 417 1038 340 1353
320 1164 307 585 302 585 307 1164 320
1996 318 476 172 272 172 476 318 1996
320 1164 307 585 302 585 307 1164 320
1353 340 1038 417 964 417 1038 340 1353
16 358 1717 279 1098 154 1098 279 1717 358
2266 368 816 167 498 167 816 368 2266
414 1018 288 296 28 296 288 1018 414
2266 368 816 167 498 167 816 368 2266
358 1717 279 1098 154 1098 279 1717 358
17 3446 984 2558 1130 2498 1130 2558 984 3446
1039 2046 809 1355 520 1355 809 2046 1039
2552 984 898 344 424 344 898 984 2552
1039 2046 809 1355 520 1355 809 2046 1039
3446 984 2558 1130 2498 1130 2558 984 3446
18 1267 3262 776 2549 350 2549 776 3262 1267
2930 1084 1730 297 1306 297 1730 1084 2930
1358 1566 584 622 128 622 584 1566 1358
2930 1084 1730 297 1306 297 1730 1084 2930
1267 3262 776 2549 350 2549 776 3262 1267
19 4378 2453 4954 2237 5532 2237 4954 2453 4378
2822 3419 1516 2597 1040 2597 1516 3419 2822
4536 2174 1622 366 1156 366 1622 2174 4536
2822 3419 1516 2597 1040 2597 1516 3419 2822
4378 2453 4954 2237 5532 2237 4954 2453 4378
20 3462 4534 1386 4891 786 4891 1386 4534 3462
5136 2053 2117 725 3314 725 2117 2053 5136
3312 2434 480 1678 528 1678 480 2434 3312
5136 2053 2117 725 3314 725 2117 2053 5136
3462 4534 1386 4891 786 4891 1386 4534 3462
21 7660 4573 6213 3782 9322 3782 6213 4573 7660
5804 5162 1892 4583 1930 4583 1892 5162 5804
7578 3210 1544 920 3368 920 1544 3210 7578
5804 5162 1892 4583 1930 4583 1892 5162 5804
7660 4573 6213 3782 9322 3782 6213 4573 7660
22 6267 6326 2506 5345 1416 5345 2506 6326 6267
7353 1776 2605 1337 5382 1337 2605 1776 7353
4906 1314 942 3752 1584 3752 942 1314 4906
7353 1776 2605 1337 5382 1337 2605 1776 7353
6267 6326 2506 5345 1416 5345 2506 6326 6267
23 10947 6763 9548 5669 7044 5669 9548 6763 10947
7351 5894 3118 5195 3366 5195 3118 5894 7351
8954 3268 1858 1832 6400 1832 1858 3268 8954
7351 5894 3118 5195 3366 5195 3118 5894 7351
10947 6763 9548 5669 7044 5669 9548 6763 10947
24 6091 7650 4113 4517 2136 4517 4113 7650 6091
5681 1864 2460 2111 2510 2111 2460 1864 5681
2058 1196 1604 4908 3480 4908 1604 1196 2058
5681 1864 2460 2111 2510 2111 2460 1864 5681
6091 7650 4113 4517 2136 4517 4113 7650 6091
25 9676 8287 9239 5938 5526 5938 9239 8287 9676
5628 4385 3915 4652 4156 4652 3915 4385 5628
7794 2034 2176 3326 4716 3326 2176 2034 7794
5628 4385 3915 4652 4156 4652 3915 4385 5628
9676 8287 9239 5938 5526 5938 9239 8287 9676
26 3743 4804 4114 3698 2350 3698 4114 4804 3743
3029 476 1934 1392 1598 1392 1934 476 3029
636 754 2358 4440 4644 4440 2358 754 636
3029 476 1934 1392 1598 1392 1934 476 3029
3743 4804 4114 3698 2350 3698 4114 4804 3743
27 4003 3461 4960 3513 3036 3513 4960 3461 4003
2412 1035 1819 2460 1700 2460 1819 1035 2412
3406 506 2174 3098 3400 3098 2174 506 3406
2412 1035 1819 2460 1700 2460 1819 1035 2412
4003 3461 4960 3513 3036 3513 4960 3461 4003
28 1239 928 319 1181 1234 1181 319 928 1239
423 4 567 442 452 442 567 4 423
8 460 1540 1630 228 1630 1540 460 8
423 4 567 442 452 442 567 4 423
1239 928 319 1181 1234 1181 319 928 1239
29 372 47 140 6 354 6 140 47 372
6 0 18 52 40 52 18 0 6
24 0 636 64 0 64 636 0 24
6 0 18 52 40 52 18 0 6
372 47 140 6 354 6 140 47 372
30 11 22 0 0 8 0 0 22 11
0 0 0 0 0 0 0 0 0
0 0 24 10 0 10 24 0 0
0 0 0 0 0 0 0 0 0
11 22 0 0 8 0 0 22 11
Total 64904 57210 52820 46787 43294 46787 52820 57210 64904
53478 31544 26459 28472 28700 28472 26459 31544 53478
50228 22432 19802 27924 30696 27924 19802 22432 50228
53478 31544 26459 28472 28700 28472 26459 31544 53478
64904 57210 52820 46787 43294 46787 52820 57210 64904
Grand total = 2*19802 + 2*22432 + 4*26459 + 2*27924 + 4*28472 + 2*28700 + 30696 + 4*31544 + 2*43294 + 4*46787 + 2*50228 + 4*52820 + 4*53478 + 4*57210 + 4*64904
= 1862152
Number of times each node is the end node (EN) in a CNSAP of each length (L)
EN 0 1 2 3 4 5 6 7 8
9 10 11 12 13 14 15 16 17
18 19 20 21 22 23 24 25 26
27 28 29 30 31 32 33 34 35
36 37 38 39 40 41 42 43 44
L
3 2 0 0 0 0 0 0 0 2
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
2 0 0 0 0 0 0 0 2
4 4 0 0 0 0 0 0 0 4
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
4 0 0 0 0 0 0 0 4
5 10 0 0 0 0 0 0 0 10
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
10 0 0 0 0 0 0 0 10
6 22 0 0 0 0 0 0 0 22
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
22 0 0 0 0 0 0 0 22
7 46 2 2 2 2 2 2 2 46
2 0 0 0 0 0 0 0 2
2 0 0 0 0 0 0 0 2
2 0 0 0 0 0 0 0 2
46 2 2 2 2 2 2 2 46
8 83 1 2 2 2 2 2 1 83
1 0 0 0 0 0 0 0 1
2 0 0 0 0 0 0 0 2
1 0 0 0 0 0 0 0 1
83 1 2 2 2 2 2 1 83
9 159 6 9 10 10 10 9 6 159
6 0 0 0 0 0 0 0 6
8 0 0 0 0 0 0 0 8
6 0 0 0 0 0 0 0 6
159 6 9 10 10 10 9 6 159
10 282 6 9 13 14 13 9 6 282
5 0 0 0 0 0 0 0 5
4 0 0 0 0 0 0 0 4
5 0 0 0 0 0 0 0 5
282 6 9 13 14 13 9 6 282
11 534 26 44 49 54 49 44 26 534
19 4 8 8 8 8 8 4 19
32 8 16 16 16 16 16 8 32
19 4 8 8 8 8 8 4 19
534 26 44 49 54 49 44 26 534
12 954 26 43 57 56 57 43 26 954
11 0 4 4 4 4 4 0 11
12 4 16 16 16 16 16 4 12
11 0 4 4 4 4 4 0 11
954 26 43 57 56 57 43 26 954
13 1740 100 174 205 216 205 174 100 1740
60 20 44 56 56 56 44 20 60
88 32 72 96 96 96 72 32 88
60 20 44 56 56 56 44 20 60
1740 100 174 205 216 205 174 100 1740
14 2614 99 164 199 188 199 164 99 2614
20 0 32 46 48 46 32 0 20
24 16 88 124 128 124 88 16 24
20 0 32 46 48 46 32 0 20
2614 99 164 199 188 199 164 99 2614
15 4271 333 571 714 780 714 571 333 4271
175 72 174 278 304 278 174 72 175
232 84 240 380 432 380 240 84 232
175 72 174 278 304 278 174 72 175
4271 333 571 714 780 714 571 333 4271
16 5410 329 492 635 618 635 492 329 5410
63 0 141 256 288 256 141 0 63
44 30 318 560 620 560 318 30 44
63 0 141 256 288 256 141 0 63
5410 329 492 635 618 635 492 329 5410
17 7849 862 1475 1865 2244 1865 1475 862 7849
445 177 500 860 1044 860 500 177 445
548 196 722 1188 1468 1188 722 196 548
445 177 500 860 1044 860 500 177 445
7849 862 1475 1865 2244 1865 1475 862 7849
18 8278 864 1255 1671 1706 1671 1255 864 8278
213 0 420 847 1068 847 420 0 213
104 42 890 1758 1952 1758 890 42 104
213 0 420 847 1068 847 420 0 213
8278 864 1255 1671 1706 1671 1255 864 8278
19 11197 1889 3286 3980 4338 3980 3286 1889 11197
1008 357 1105 2105 2260 2105 1105 357 1008
1200 414 1806 2998 3460 2998 1806 414 1200
1008 357 1105 2105 2260 2105 1105 357 1008
11197 1889 3286 3980 4338 3980 3286 1889 11197
20 12020 1770 2679 3486 3232 3486 2679 1770 12020
517 0 920 1890 2586 1890 920 0 517
272 76 1856 4046 4488 4046 1856 76 272
517 0 920 1890 2586 1890 920 0 517
12020 1770 2679 3486 3232 3486 2679 1770 12020
21 14999 3592 6339 6326 6660 6326 6339 3592 14999
1976 674 2133 3533 3898 3533 2133 674 1976
2558 880 3646 5330 6820 5330 3646 880 2558
1976 674 2133 3533 3898 3533 2133 674 1976
14999 3592 6339 6326 6660 6326 6339 3592 14999
22 13758 2850 4502 5284 4166 5284 4502 2850 13758
887 0 1620 2621 3562 2621 1620 0 887
662 190 3636 6794 6960 6794 3636 190 662
887 0 1620 2621 3562 2621 1620 0 887
13758 2850 4502 5284 4166 5284 4502 2850 13758
23 15669 6061 9012 7783 7792 7783 9012 6061 15669
3930 1350 3115 4531 3584 4531 3115 1350 3930
5328 1860 5720 7046 8520 7046 5720 1860 5328
3930 1350 3115 4531 3584 4531 3115 1350 3930
15669 6061 9012 7783 7792 7783 9012 6061 15669
24 10366 3584 4876 5559 4630 5559 4876 3584 10366
1529 0 2108 2385 2198 2385 2108 0 1529
1332 458 5152 7680 5724 7680 5152 458 1332
1529 0 2108 2385 2198 2385 2108 0 1529
10366 3584 4876 5559 4630 5559 4876 3584 10366
25 11535 6688 8481 7614 7220 7614 8481 6688 11535
4657 1541 3393 4029 3650 4029 3393 1541 4657
6128 2178 6358 6520 5760 6520 6358 2178 6128
4657 1541 3393 4029 3650 4029 3393 1541 4657
11535 6688 8481 7614 7220 7614 8481 6688 11535
26 5663 2541 3520 4047 4014 4047 3520 2541 5663
1560 0 1680 1765 1588 1765 1680 0 1560
860 684 5248 5188 3408 5188 5248 684 860
1560 0 1680 1765 1588 1765 1680 0 1560
5663 2541 3520 4047 4014 4047 3520 2541 5663
27 4769 3102 3863 3683 4010 3683 3863 3102 4769
2141 739 1783 2232 1854 2232 1783 739 2141
2644 844 3994 3598 2756 3598 3994 844 2644
2141 739 1783 2232 1854 2232 1783 739 2141
4769 3102 3863 3683 4010 3683 3863 3102 4769
28 1553 666 453 1023 1548 1023 453 666 1553
241 0 472 468 404 468 472 0 241
24 400 2136 1296 168 1296 2136 400 24
241 0 472 468 404 468 472 0 241
1553 666 453 1023 1548 1023 453 666 1553
29 361 62 140 6 362 6 140 62 361
2 0 10 52 32 52 10 0 2
24 0 650 66 0 66 650 0 24
2 0 10 52 32 52 10 0 2
361 62 140 6 362 6 140 62 361
30 11 22 0 0 8 0 0 22 11
0 0 0 0 0 0 0 0 0
0 0 24 10 0 10 24 0 0
0 0 0 0 0 0 0 0 0
11 22 0 0 8 0 0 22 11
Total 134159 35481 51391 54213 53870 54213 51391 35481 134159
19468 4934 19662 27966 28436 27966 19662 4934 19468
22132 8396 42588 54710 52792 54710 42588 8396 22132
19468 4934 19662 27966 28436 27966 19662 4934 19468
134159 35481 51391 54213 53870 54213 51391 35481 134159
Grand total = 4*4934 + 2*8396 + 4*19468 + 4*19662 + 2*22132 + 4*27966 + 2*28436 + 4*35481 + 2*42588 + 4*51391 + 52792 + 2*53870 + 4*54213 + 2*54710 + 4*134159
= 1862152
Number of times each node (N) is present in a CNSAP of each length (L)
N 0 1 2 3 4 5 6 7 8
9 10 11 12 13 14 15 16 17
18 19 20 21 22 23 24 25 26
27 28 29 30 31 32 33 34 35
36 37 38 39 40 41 42 43 44
L
3 2 1 0 0 0 0 0 1 2
1 2 0 0 0 0 0 2 1
0 0 0 0 0 0 0 0 0
1 2 0 0 0 0 0 2 1
2 1 0 0 0 0 0 1 2
4 4 2 0 0 0 0 0 2 4
2 4 2 0 0 0 2 4 2
0 4 0 0 0 0 0 4 0
2 4 2 0 0 0 2 4 2
4 2 0 0 0 0 0 2 4
5 10 5 1 0 0 0 1 5 10
5 12 5 2 0 2 5 12 5
2 10 8 0 0 0 8 10 2
5 12 5 2 0 2 5 12 5
10 5 1 0 0 0 1 5 10
6 22 13 1 3 0 3 1 13 22
14 28 17 6 4 6 17 28 14
2 22 16 12 0 12 16 22 2
14 28 17 6 4 6 17 28 14
22 13 1 3 0 3 1 13 22
7 53 32 17 7 14 7 17 32 53
31 60 47 32 16 32 47 60 31
14 58 62 40 44 40 62 58 14
31 60 47 32 16 32 47 60 31
53 32 17 7 14 7 17 32 53
8 86 54 20 38 16 38 20 54 86
50 101 89 68 84 68 89 101 50
10 78 106 104 92 104 106 78 10
50 101 89 68 84 68 89 101 50
86 54 20 38 16 38 20 54 86
9 183 113 70 79 144 79 70 113 183
113 208 189 213 204 213 189 208 113
44 166 264 278 292 278 264 166 44
113 208 189 213 204 213 189 208 113
183 113 70 79 144 79 70 113 183
10 308 202 91 218 220 218 91 202 308
180 352 374 391 448 391 374 352 180
34 294 412 550 580 550 412 294 34
180 352 374 391 448 391 374 352 180
308 202 91 218 220 218 91 202 308
11 641 456 479 520 554 520 479 456 641
441 915 950 1138 1066 1138 950 915 441
252 706 1068 1360 1400 1360 1068 706 252
441 915 950 1138 1066 1138 950 915 441
641 456 479 520 554 520 479 456 641
12 1057 941 631 866 880 866 631 941 1057
781 1537 1674 1708 1798 1708 1674 1537 781
220 1398 1808 2164 2220 2164 1808 1398 220
781 1537 1674 1708 1798 1708 1674 1537 781
1057 941 631 866 880 866 631 941 1057
13 2519 2143 2176 2542 2810 2542 2176 2143 2519
1840 3799 3873 4387 4612 4387 3873 3799 1840
1424 3270 4276 4760 5136 4760 4276 3270 1424
1840 3799 3873 4387 4612 4387 3873 3799 1840
2519 2143 2176 2542 2810 2542 2176 2143 2519
14 3207 3110 2696 3700 3884 3700 2696 3110 3207
3015 5377 5597 5644 5858 5644 5597 5377 3015
1474 5568 6230 6030 5728 6030 6230 5568 1474
3015 5377 5597 5644 5858 5644 5597 5377 3015
3207 3110 2696 3700 3884 3700 2696 3110 3207
15 7125 7072 8484 10516 12042 10516 8484 7072 7125
6433 12026 12180 13263 14268 13263 12180 12026 6433
6190 11956 12934 12818 13548 12818 12934 11956 6190
6433 12026 12180 13263 14268 13263 12180 12026 6433
7125 7072 8484 10516 12042 10516 8484 7072 7125
16 7901 9208 9411 12484 12980 12484 9411 9208 7901
8781 14521 14785 14296 14270 14296 14785 14521 8781
6888 15562 15904 14212 13060 14212 15904 15562 6888
8781 14521 14785 14296 14270 14296 14785 14521 8781
7901 9208 9411 12484 12980 12484 9411 9208 7901
17 16569 19535 25124 31167 34026 31167 25124 19535 16569
17969 29754 30468 32320 29976 32320 30468 29754 17969
18090 30416 30806 29038 24900 29038 30806 30416 18090
17969 29754 30468 32320 29976 32320 30468 29754 17969
16569 19535 25124 31167 34026 31167 25124 19535 16569
18 17072 22783 25218 30450 30562 30450 25218 22783 17072
21142 31553 31942 30258 30116 30258 31942 31553 21142
20240 32216 30968 27794 25576 27794 30968 32216 20240
21142 31553 31942 30258 30116 30258 31942 31553 21142
17072 22783 25218 30450 30562 30450 25218 22783 17072
19 31126 45086 60098 67167 71742 67167 60098 45086 31126
41722 61610 64619 59091 57198 59091 64619 61610 41722
46076 62904 61404 45746 42584 45746 61404 62904 46076
41722 61610 64619 59091 57198 59091 64619 61610 41722
31126 45086 60098 67167 71742 67167 60098 45086 31126
20 34461 49991 57506 64984 64342 64984 57506 49991 34461
47360 62834 58752 54842 56490 54842 58752 62834 47360
49544 63548 53426 46548 44324 46548 53426 63548 49544
47360 62834 58752 54842 56490 54842 58752 62834 47360
34461 49991 57506 64984 64342 64984 57506 49991 34461
21 59029 92581 114211 123595 129388 123595 114211 92581 59029
87831 117388 100568 97172 96348 97172 100568 117388 87831
101818 121810 82440 66114 66756 66114 82440 121810 101818
87831 117388 100568 97172 96348 97172 100568 117388 87831
59029 92581 114211 123595 129388 123595 114211 92581 59029
22 57025 83440 94910 103369 102788 103369 94910 83440 57025
85349 94321 80069 77547 81614 77547 80069 94321 85349
94980 93006 64664 61800 61672 61800 64664 93006 94980
85349 94321 80069 77547 81614 77547 80069 94321 85349
57025 83440 94910 103369 102788 103369 94910 83440 57025
23 96645 144355 173474 176380 173864 176380 173474 144355 96645
158568 155058 130409 131143 132760 131143 130409 155058 158568
191344 148484 86102 77012 87372 77012 86102 148484 191344
158568 155058 130409 131143 132760 131143 130409 155058 158568
96645 144355 173474 176380 173864 176380 173474 144355 96645
24 68279 100324 111722 109800 104094 109800 111722 100324 68279
108532 94283 78484 78701 81480 78701 78484 94283 108532
124532 83848 51904 61904 70024 61904 51904 83848 124532
108532 94283 78484 78701 81480 78701 78484 94283 108532
68279 100324 111722 109800 104094 109800 111722 100324 68279
25 116528 168359 191702 169027 152478 169027 191702 168359 116528
187890 135498 124699 132577 137862 132577 124699 135498 187890
226570 109310 64672 79650 94296 79650 64672 109310 226570
187890 135498 124699 132577 137862 132577 124699 135498 187890
116528 168359 191702 169027 152478 169027 191702 168359 116528
26 62076 86946 94452 80208 71518 80208 94452 86946 62076
94187 58869 54293 57185 59824 57185 54293 58869 94187
109422 48752 35390 51050 58800 51050 35390 48752 109422
94187 58869 54293 57185 59824 57185 54293 58869 94187
62076 86946 94452 80208 71518 80208 94452 86946 62076
27 70865 101556 112586 84417 68184 84417 112586 101556 70865
101373 53421 54174 61410 60604 61410 54174 53421 101373
120488 42016 32192 60352 72204 60352 32192 42016 120488
101373 53421 54174 61410 60604 61410 54174 53421 101373
70865 101556 112586 84417 68184 84417 112586 101556 70865
28 20036 26845 28460 21277 17796 21277 28460 26845 20036
25994 11561 13685 15372 15424 15372 13685 11561 25994
30262 10580 11260 17410 17680 17410 11260 10580 30262
25994 11561 13685 15372 15424 15372 13685 11561 25994
20036 26845 28460 21277 17796 21277 28460 26845 20036
29 3465 4316 4516 3146 3526 3146 4516 4316 3465
4156 1490 1944 2102 2460 2102 1944 1490 4156
4766 1232 3084 3042 2440 3042 3084 1232 4766
4156 1490 1944 2102 2460 2102 1944 1490 4156
3465 4316 4516 3146 3526 3146 4516 4316 3465
30 180 208 170 144 192 144 170 208 180
202 38 124 78 128 78 124 38 202
216 28 192 108 176 108 192 28 216
202 38 124 78 128 78 124 38 202
180 208 170 144 192 144 170 208 180
Total 676474 969677 1118226 1096104 1058044 1096104 1118226 969677 676474
1003962 946620 864012 870946 884912 870946 864012 946620 1003962
1154902 887242 651592 669896 710904 669896 651592 887242 1154902
1003962 946620 864012 870946 884912 870946 864012 946620 1003962
676474 969677 1118226 1096104 1058044 1096104 1118226 969677 676474
Grand total = 2*651592 + 2*669896 + 4*676474 + 710904 + 4*864012 + 4*870946 + 2*884912 + 2*887242 + 4*946620 + 4*969677 + 4*1003962 + 2*1058044 + 4*1096104 + 4*1118226 + 2*1154902
= 41508164
Number of CNSAPs for each start node (SN) and end node (EN) pair
SN 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44
EN
0 0 0 6826 5375 4760 3900 3924 4131 4705 0 2 1527 3458 3577 2595 1989 2170 3705 6776 912 681 2031 2604 2447 1847 1704 3473 5657 2614 1497 1120 1300 2103 2462 2577 4011 5636 3951 2658 2089 2471 3781 4790 4972 5351
1 0 0 0 5133 181 314 361 813 945 5105 0 2587 1686 3 29 204 453 785 0 0 924 584 644 820 444 363 781 0 0 0 335 983 954 644 558 959 389 389 389 736 1218 1176 1169 1125 1298
2 5157 0 0 0 5430 214 594 674 990 1720 4000 0 3933 1870 20 114 468 984 0 0 568 1593 620 940 838 556 1132 142 0 0 0 696 1874 1416 1012 1548 284 284 284 568 1632 2598 2328 2078 2232
3 2766 5333 0 0 0 5007 477 799 885 705 607 2887 0 3680 1525 116 371 1000 705 0 578 1043 1528 474 730 686 1239 754 333 0 0 0 959 1815 1348 1682 754 916 569 383 922 2406 3176 2551 2504
4 1404 1166 5081 0 0 0 5081 1166 1404 1038 303 1122 2950 0 2950 1122 303 1038 1135 489 256 1132 1118 1132 256 489 1135 1347 1136 706 0 0 0 706 1136 1347 1784 2129 1989 962 494 962 1989 2129 1784
5 885 799 477 5007 0 0 0 5333 2766 1000 371 116 1525 3680 0 2887 607 705 1239 686 730 474 1528 1043 578 0 705 1682 1348 1815 959 0 0 0 333 754 2504 2551 3176 2406 922 383 569 916 754
6 990 674 594 214 5430 0 0 0 5157 984 468 114 20 1870 3933 0 4000 1720 1132 556 838 940 620 1593 568 0 0 1548 1012 1416 1874 696 0 0 0 142 2232 2078 2328 2598 1632 568 284 284 284
7 945 813 361 314 181 5133 0 0 0 785 453 204 29 3 1686 2587 0 5105 781 363 444 820 644 584 924 0 0 959 558 644 954 983 335 0 0 0 1298 1125 1169 1176 1218 736 389 389 389
8 4705 4131 3924 3900 4760 5375 6826 0 0 3705 2170 1989 2595 3577 3458 1527 2 0 3473 1704 1847 2447 2604 2031 681 912 6776 4011 2577 2462 2103 1300 1120 1497 2614 5657 5351 4972 4790 3781 2471 2089 2658 3951 5636
9 0 5105 0 0 191 214 207 209 249 0 0 0 0 185 158 109 109 193 0 2291 295 105 144 99 84 88 179 4805 286 0 1 3 6 102 137 204 2268 286 213 71 22 88 227 264 271
10 0 0 2280 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2654 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
11 1788 1952 0 1898 498 236 245 261 325 1788 0 0 0 950 19 127 151 307 922 1510 0 506 351 91 208 186 358 0 0 0 0 0 366 499 348 478 0 0 0 0 297 790 823 686 698
12 1912 1784 2692 0 1922 900 494 608 682 1020 1432 0 0 0 1604 114 330 602 352 352 776 0 820 524 128 336 688 352 0 0 0 0 0 600 752 876 352 220 0 0 0 638 1496 1356 1252
13 1293 912 1353 2424 0 2424 1353 912 1293 837 381 1617 0 0 0 1617 381 837 628 134 434 687 0 687 434 134 628 762 402 0 0 0 0 0 402 762 896 972 486 0 0 0 486 972 896
14 682 608 494 900 1922 0 2692 1784 1912 602 330 114 1604 0 0 0 1432 1020 688 336 128 524 820 0 776 352 352 876 752 600 0 0 0 0 0 352 1252 1356 1496 638 0 0 0 220 352
15 325 261 245 236 498 1898 0 1952 1788 307 151 127 19 950 0 0 0 1788 358 186 208 91 351 506 0 1510 922 478 348 499 366 0 0 0 0 0 698 686 823 790 297 0 0 0 0
16 0 0 0 0 0 0 2280 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2654 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
17 249 209 207 214 191 0 0 5105 0 193 109 109 158 185 0 0 0 0 179 88 84 99 144 105 295 2291 0 204 137 102 6 3 1 0 286 4805 271 264 227 88 22 71 213 286 2268
18 5072 1670 0 0 0 0 0 0 0 0 4324 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4324 0 0 0 0 0 0 0 5072 1670 0 0 0 0 0 0 0
19 615 615 335 0 0 0 0 0 0 1710 0 923 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1710 0 923 0 0 0 0 0 0 615 615 335 0 0 0 0 0 0
20 1552 1950 1228 660 428 912 1416 1480 1620 1948 1156 0 636 304 408 708 772 1240 2344 0 0 0 808 408 520 552 1120 1948 1156 0 636 304 408 708 772 1240 1552 1950 1228 660 428 912 1416 1480 1620
21 2200 1656 2046 1207 934 751 1524 2191 2409 1570 1112 1310 0 799 519 572 1148 1848 1508 1260 0 0 0 1364 516 806 1664 1570 1112 1310 0 799 519 572 1148 1848 2200 1656 2046 1207 934 751 1524 2191 2409
22 2366 1722 1140 1356 988 1356 1140 1722 2366 1796 752 692 1214 0 1214 692 752 1796 1548 600 1184 0 0 0 1184 600 1548 1796 752 692 1214 0 1214 692 752 1796 2366 1722 1140 1356 988 1356 1140 1722 2366
23 2409 2191 1524 751 934 1207 2046 1656 2200 1848 1148 572 519 799 0 1310 1112 1570 1664 806 516 1364 0 0 0 1260 1508 1848 1148 572 519 799 0 1310 1112 1570 2409 2191 1524 751 934 1207 2046 1656 2200
24 1620 1480 1416 912 428 660 1228 1950 1552 1240 772 708 408 304 636 0 1156 1948 1120 552 520 408 808 0 0 0 2344 1240 772 708 408 304 636 0 1156 1948 1620 1480 1416 912 428 660 1228 1950 1552
25 0 0 0 0 0 0 335 615 615 0 0 0 0 0 0 923 0 1710 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 923 0 1710 0 0 0 0 0 0 335 615 615
26 0 0 0 0 0 0 0 1670 5072 0 0 0 0 0 0 0 4324 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4324 0 0 0 0 0 0 0 0 1670 5072
27 2268 286 213 71 22 88 227 264 271 4805 286 0 1 3 6 102 137 204 0 2291 295 105 144 99 84 88 179 0 0 0 0 185 158 109 109 193 0 5105 0 0 191 214 207 209 249
28 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2654 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2280 0 0 0 0 0 0
29 0 0 0 0 297 790 823 686 698 0 0 0 0 0 366 499 348 478 922 1510 0 506 351 91 208 186 358 1788 0 0 0 950 19 127 151 307 1788 1952 0 1898 498 236 245 261 325
30 352 220 0 0 0 638 1496 1356 1252 352 0 0 0 0 0 600 752 876 352 352 776 0 820 524 128 336 688 1020 1432 0 0 0 1604 114 330 602 1912 1784 2692 0 1922 900 494 608 682
31 896 972 486 0 0 0 486 972 896 762 402 0 0 0 0 0 402 762 628 134 434 687 0 687 434 134 628 837 381 1617 0 0 0 1617 381 837 1293 912 1353 2424 0 2424 1353 912 1293
32 1252 1356 1496 638 0 0 0 220 352 876 752 600 0 0 0 0 0 352 688 336 128 524 820 0 776 352 352 602 330 114 1604 0 0 0 1432 1020 682 608 494 900 1922 0 2692 1784 1912
33 698 686 823 790 297 0 0 0 0 478 348 499 366 0 0 0 0 0 358 186 208 91 351 506 0 1510 922 307 151 127 19 950 0 0 0 1788 325 261 245 236 498 1898 0 1952 1788
34 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2654 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2280 0 0
35 271 264 227 88 22 71 213 286 2268 204 137 102 6 3 1 0 286 4805 179 88 84 99 144 105 295 2291 0 193 109 109 158 185 0 0 0 0 249 209 207 214 191 0 0 5105 0
36 5636 3951 2658 2089 2471 3781 4790 4972 5351 5657 2614 1497 1120 1300 2103 2462 2577 4011 6776 912 681 2031 2604 2447 1847 1704 3473 0 2 1527 3458 3577 2595 1989 2170 3705 0 0 6826 5375 4760 3900 3924 4131 4705
37 389 389 389 736 1218 1176 1169 1125 1298 0 0 0 335 983 954 644 558 959 0 0 924 584 644 820 444 363 781 5105 0 2587 1686 3 29 204 453 785 0 0 0 5133 181 314 361 813 945
38 284 284 284 568 1632 2598 2328 2078 2232 142 0 0 0 696 1874 1416 1012 1548 0 0 568 1593 620 940 838 556 1132 1720 4000 0 3933 1870 20 114 468 984 5157 0 0 0 5430 214 594 674 990
39 754 916 569 383 922 2406 3176 2551 2504 754 333 0 0 0 959 1815 1348 1682 705 0 578 1043 1528 474 730 686 1239 705 607 2887 0 3680 1525 116 371 1000 2766 5333 0 0 0 5007 477 799 885
40 1784 2129 1989 962 494 962 1989 2129 1784 1347 1136 706 0 0 0 706 1136 1347 1135 489 256 1132 1118 1132 256 489 1135 1038 303 1122 2950 0 2950 1122 303 1038 1404 1166 5081 0 0 0 5081 1166 1404
41 2504 2551 3176 2406 922 383 569 916 754 1682 1348 1815 959 0 0 0 333 754 1239 686 730 474 1528 1043 578 0 705 1000 371 116 1525 3680 0 2887 607 705 885 799 477 5007 0 0 0 5333 2766
42 2232 2078 2328 2598 1632 568 284 284 284 1548 1012 1416 1874 696 0 0 0 142 1132 556 838 940 620 1593 568 0 0 984 468 114 20 1870 3933 0 4000 1720 990 674 594 214 5430 0 0 0 5157
43 1298 1125 1169 1176 1218 736 389 389 389 959 558 644 954 983 335 0 0 0 781 363 444 820 644 584 924 0 0 785 453 204 29 3 1686 2587 0 5105 945 813 361 314 181 5133 0 0 0
44 5351 4972 4790 3781 2471 2089 2658 3951 5636 4011 2577 2462 2103 1300 1120 1497 2614 5657 3473 1704 1847 2447 2604 2031 681 912 6776 3705 2170 1989 2595 3577 3458 1527 2 0 4705 4131 3924 3900 4760 5375 6826 0 0
Sum of all rows = 4(3*0 + 1*2 + 1*681 + 1*912 + 1*1120 + 1*1300 + 1*1497 + 1*1527 + 1*1704 + 1*1847 + 1*1989 + 1*2031 + 1*2089 + 1*2103 + 1*2170 + 1*2447 + 1*2462 + 1*2471 + 1*2577 + 1*2595 + 1*2604 + 1*2614 +
1*2658 + 1*3458 + 1*3473 + 1*3577 + 1*3705 + 1*3781 + 1*3900 + 1*3924 + 1*3951 + 1*4011 + 1*4131 + 1*4705 + 1*4760 + 1*4790 + 1*4972 + 1*5351 + 1*5375 + 1*5636 + 1*5657 + 1*6776 + 1*6826) +
4(9*0 + 1*3 + 1*29 + 1*181 + 1*204 + 1*314 + 1*335 + 1*361 + 1*363 + 3*389 + 1*444 + 1*453 + 1*558 + 1*584 + 2*644 + 1*736 + 1*781 + 1*785 + 1*813 + 1*820 + 1*924 + 1*945 + 1*954 + 1*959 +
1*983 + 1*1125 + 1*1169 + 1*1176 + 1*1218 + 1*1298 + 1*1686 + 1*2587 + 1*5105 + 1*5133) +
4(9*0 + 1*20 + 1*114 + 1*142 + 1*214 + 3*284 + 1*468 + 1*556 + 2*568 + 1*594 + 1*620 + 1*674 + 1*696 + 1*838 + 1*940 + 1*984 + 1*990 + 1*1012 + 1*1132 + 1*1416 + 1*1548 + 1*1593 + 1*1632 +
1*1720 + 1*1870 + 1*1874 + 1*2078 + 1*2232 + 1*2328 + 1*2598 + 1*3933 + 1*4000 + 1*5157 + 1*5430) +
4(8*0 + 1*116 + 1*333 + 1*371 + 1*383 + 1*474 + 1*477 + 1*569 + 1*578 + 1*607 + 1*686 + 2*705 + 1*730 + 2*754 + 1*799 + 1*885 + 1*916 + 1*922 + 1*959 + 1*1000 + 1*1043 + 1*1239 + 1*1348 +
1*1525 + 1*1528 + 1*1682 + 1*1815 + 1*2406 + 1*2504 + 1*2551 + 1*2766 + 1*2887 + 1*3176 + 1*3680 + 1*5007 + 1*5333) +
2(7*0 + 2*256 + 2*303 + 2*489 + 1*494 + 2*706 + 2*962 + 2*1038 + 1*1118 + 2*1122 + 2*1132 + 2*1135 + 2*1136 + 2*1166 + 2*1347 + 2*1404 + 2*1784 + 2*1989 + 2*2129 + 2*2950 + 2*5081) +
4(10*0 + 1*1 + 1*3 + 1*6 + 1*22 + 1*71 + 1*84 + 2*88 + 1*99 + 1*102 + 1*105 + 2*109 + 1*137 + 1*144 + 1*158 + 1*179 + 1*185 + 1*191 + 1*193 + 1*204 + 1*207 + 1*209 + 1*213 + 1*214 + 1*227 +
1*249 + 1*264 + 1*271 + 2*286 + 1*295 + 1*2268 + 1*2291 + 1*4805 + 1*5105) +
4(43*0 + 1*2280 + 1*2654) +
4(14*0 + 1*19 + 1*91 + 1*127 + 1*151 + 1*186 + 1*208 + 1*236 + 1*245 + 1*261 + 1*297 + 1*307 + 1*325 + 1*348 + 1*351 + 1*358 + 1*366 + 1*478 + 1*498 + 1*499 + 1*506 + 1*686 + 1*698 + 1*790 +
1*823 + 1*922 + 1*950 + 1*1510 + 2*1788 + 1*1898 + 1*1952) +
4(13*0 + 1*114 + 1*128 + 1*220 + 1*330 + 1*336 + 4*352 + 1*494 + 1*524 + 1*600 + 1*602 + 1*608 + 1*638 + 1*682 + 1*688 + 1*752 + 1*776 + 1*820 + 1*876 + 1*900 + 1*1020 + 1*1252 + 1*1356 +
1*1432 + 1*1496 + 1*1604 + 1*1784 + 1*1912 + 1*1922 + 1*2692) +
2(13*0 + 2*134 + 2*381 + 2*402 + 2*434 + 2*486 + 2*628 + 2*687 + 2*762 + 2*837 + 2*896 + 2*912 + 2*972 + 2*1293 + 2*1353 + 2*1617 + 2*2424) +
2(39*0 + 2*1670 + 2*4324 + 2*5072) +
2(35*0 + 2*335 + 4*615 + 2*923 + 2*1710) +
2(5*0 + 2*304 + 3*408 + 2*428 + 1*520 + 1*552 + 2*636 + 2*660 + 2*708 + 2*772 + 1*808 + 2*912 + 1*1120 + 2*1156 + 2*1228 + 2*1240 + 2*1416 + 2*1480 + 2*1552 + 2*1620 + 2*1948 + 2*1950 + 1*2344) +
2(5*0 + 1*516 + 2*519 + 2*572 + 2*751 + 2*799 + 1*806 + 2*934 + 2*1112 + 2*1148 + 2*1207 + 1*1260 + 2*1310 + 1*1364 + 1*1508 + 2*1524 + 2*1570 + 2*1656 + 1*1664 + 2*1848 + 2*2046 + 2*2191 +
2*2200 + 2*2409) +
1(5*0 + 2*600 + 4*692 + 4*752 + 2*988 + 4*1140 + 2*1184 + 4*1214 + 4*1356 + 2*1548 + 4*1722 + 4*1796 + 4*2366)
= 536636 + 141924 + 205564 + 216852 + 107740 + 77872 + 19736 + 78648 + 111864 + 56872 + 44264 + 16792 + 85176 + 109420 + 52792
= 1862152
Value repetition frequencies = 4(42*1 + 1*3) +
4(31*1 + 1*2 + 1*3 + 1*9) +
4(31*1 + 1*2 + 1*3 + 1*9) +
4(33*1 + 2*2 + 1*8) +
2(2*1 + 18*2 + 1*7) +
4(30*1 + 3*2 + 1*9) +
4(2*1 + 1*43) +
4(29*1 + 1*2 + 1*14) +
4(28*1 + 1*4 + 1*13) +
2(16*2 + 1*13) +
2(3*2 + 1*39) +
2(3*2 + 1*4 + 1*35) +
2(5*1 + 16*2 + 1*3 + 1*5) +
2(6*1 + 17*2 + 1*5) +
1(4*2 + 8*4 + 1*5)
= 2025
Number of distinct row element sets = 15
Number of rows = 1*1 + 6*2 + 8*4
= 45
Number of distinct values = 315
Distinct values 0 1 2 3 6 19 20 22 29 71 84 88 91 99 102 105 109 114 116 127
Frequency 645 4 4 8 4 4 4 4 4 4 4 8 4 4 4 4 8 8 4 4
Distinct values 128 134 137 142 144 151 158 179 181 185 186 191 193 204 207 208 209 213 214 220
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 8 4 4 4 4 8 4
Distinct values 227 236 245 249 256 261 264 271 284 286 295 297 303 304 307 314 325 330 333 335
Frequency 4 4 4 4 4 4 4 4 12 8 4 4 4 4 4 4 4 4 4 8
Distinct values 336 348 351 352 358 361 363 366 371 381 383 389 402 408 428 434 444 453 468 474
Frequency 4 4 4 16 4 4 4 4 4 4 4 12 4 6 4 4 4 4 4 4
Distinct values 477 478 486 489 494 498 499 506 516 519 520 524 552 556 558 568 569 572 578 584
Frequency 4 4 4 4 6 4 4 4 2 4 2 4 2 4 4 8 4 4 4 4
Distinct values 594 600 602 607 608 615 620 628 636 638 644 660 674 681 682 686 687 688 692 696
Frequency 4 6 4 4 4 8 4 4 4 4 8 4 4 4 4 8 4 4 4 4
Distinct values 698 705 706 708 730 736 751 752 754 762 772 776 781 785 790 799 806 808 813 820
Frequency 4 8 4 4 4 4 4 8 8 4 4 4 4 4 4 8 2 2 4 8
Distinct values 823 837 838 876 885 896 900 912 916 922 923 924 934 940 945 950 954 959 962 972
Frequency 4 4 4 4 4 4 4 12 4 8 4 4 4 4 4 4 4 8 4 4
Distinct values 983 984 988 990 1000 1012 1020 1038 1043 1112 1118 1120 1122 1125 1132 1135 1136 1140 1148 1156
Frequency 4 4 2 4 4 4 4 4 4 4 2 6 4 4 8 4 4 4 4 4
Distinct values 1166 1169 1176 1184 1207 1214 1218 1228 1239 1240 1252 1260 1293 1298 1300 1310 1347 1348 1353 1356
Frequency 4 4 4 2 4 4 4 4 4 4 4 2 4 4 4 4 4 4 4 8
Distinct values 1364 1404 1416 1432 1480 1496 1497 1508 1510 1524 1525 1527 1528 1548 1552 1570 1593 1604 1617 1620
Frequency 2 4 8 4 4 4 4 2 4 4 4 4 4 6 4 4 4 4 4 4
Distinct values 1632 1656 1664 1670 1682 1686 1704 1710 1720 1722 1784 1788 1796 1815 1847 1848 1870 1874 1898 1912
Frequency 4 4 2 4 4 4 4 4 4 4 8 8 4 4 4 4 4 4 4 4
Distinct values 1922 1948 1950 1952 1989 2031 2046 2078 2089 2103 2129 2170 2191 2200 2232 2268 2280 2291 2328 2344
Frequency 4 4 4 4 8 4 4 4 4 4 4 4 4 4 4 4 4 4 4 2
Distinct values 2366 2406 2409 2424 2447 2462 2471 2504 2551 2577 2587 2595 2598 2604 2614 2654 2658 2692 2766 2887
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 2950 3176 3458 3473 3577 3680 3705 3781 3900 3924 3933 3951 4000 4011 4131 4324 4705 4760 4790 4805
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 4972 5007 5072 5081 5105 5133 5157 5333 5351 5375 5430 5636 5657 6776 6826
Frequency 4 4 4 4 8 4 4 4 4 4 4 4 4 4 4
Sum of distinct value frequencies = 13*2 + 266*4 + 5*6 + 26*8 + 3*12 + 1*16 + 1*645
= 2025
Number of SN-EN pairs for which the number of CNSAPs is greater than zero = 4*2 + 2*6 + 2*10 + 4*31 + 6*32 + 12*36 + 4*37 + 2*38 + 5*40 + 4*42
= 1380
Number of SN-EN pairs, with SN != EN, for which the number of CNSAPs equals zero = 600
Number of possible SN-EN pairs with SN != EN = 45*44
= 1980
a = 10, b = 5
L C
3 8
4 16
5 40
6 88
7 228
8 368
9 816
10 1324
11 3204
12 4932
13 12280
14 18148
15 40552
16 54080
17 103116
18 124908
19 210652
20 239640
21 399836
22 416708
23 655248
24 576036
25 891124
26 615688
27 993252
28 517088
29 642560
30 213252
31 66588
32 11936
33 748
34 4
Total 6814468
Number of times each node is the start node (SN) in a CNSAP of each length (L)
SN 0 1 2 3 4 5 6 7 8 9
10 11 12 13 14 15 16 17 18 19
20 21 22 23 24 25 26 27 28 29
30 31 32 33 34 35 36 37 38 39
40 41 42 43 44 45 46 47 48 49
L
3 0 0 0 0 0 0 0 0 0 0
0 2 0 0 0 0 0 0 2 0
0 0 0 0 0 0 0 0 0 0
0 2 0 0 0 0 0 0 2 0
0 0 0 0 0 0 0 0 0 0
4 0 0 0 0 0 0 0 0 0 0
0 0 2 0 0 0 0 2 0 0
0 4 0 0 0 0 0 0 4 0
0 0 2 0 0 0 0 2 0 0
0 0 0 0 0 0 0 0 0 0
5 0 0 1 0 0 0 0 1 0 0
0 2 0 2 0 0 2 0 2 0
2 0 8 0 0 0 0 8 0 2
0 2 0 2 0 0 2 0 2 0
0 0 1 0 0 0 0 1 0 0
6 0 2 0 3 0 0 3 0 2 0
3 0 6 0 2 2 0 6 0 3
0 0 0 12 0 0 12 0 0 0
3 0 6 0 2 2 0 6 0 3
0 2 0 3 0 0 3 0 2 0
7 5 1 9 0 5 5 0 9 1 5
1 4 2 16 4 4 16 2 4 1
2 2 0 0 16 16 0 0 2 2
1 4 2 16 4 4 16 2 4 1
5 1 9 0 5 5 0 9 1 5
8 0 8 0 23 7 7 23 0 8 0
4 2 3 4 29 29 4 3 2 4
0 0 0 4 20 20 4 0 0 0
4 2 3 4 29 29 4 3 2 4
0 8 0 23 7 7 23 0 8 0
9 13 5 14 13 53 53 13 14 5 13
5 7 6 11 52 52 11 6 7 5
6 2 0 24 18 18 24 0 2 6
5 7 6 11 52 52 11 6 7 5
13 5 14 13 53 53 13 14 5 13
10 6 16 15 21 97 97 21 15 16 6
10 6 6 75 29 29 75 6 6 10
2 2 30 8 58 58 8 30 2 2
10 6 6 75 29 29 75 6 6 10
6 16 15 21 97 97 21 15 16 6
11 33 36 39 179 59 59 179 39 36 33
22 31 124 41 107 107 41 124 31 22
26 46 8 136 44 44 136 8 46 26
22 31 124 41 107 107 41 124 31 22
33 36 39 179 59 59 179 39 36 33
12 38 39 265 57 103 103 57 265 39 38
32 158 26 216 65 65 216 26 158 32
50 14 254 28 122 122 28 254 14 50
32 158 26 216 65 65 216 26 158 32
38 39 265 57 103 103 57 265 39 38
13 85 465 145 321 216 216 321 145 465 85
266 112 525 143 235 235 143 525 112 266
110 484 52 352 116 116 352 52 484 110
266 112 525 143 235 235 143 525 112 266
85 465 145 321 216 216 321 145 465 85
14 615 118 587 196 309 309 196 587 118 615
124 952 121 381 172 172 381 121 952 124
746 98 812 90 178 178 90 812 98 746
124 952 121 381 172 172 381 121 952 124
615 118 587 196 309 309 196 587 118 615
15 280 1460 519 1007 755 755 1007 519 1460 280
1869 399 1127 439 583 583 439 1127 399 1869
416 1940 260 486 298 298 486 260 1940 416
1869 399 1127 439 583 583 439 1127 399 1869
280 1460 519 1007 755 755 1007 519 1460 280
16 2595 462 1680 607 846 846 607 1680 462 2595
493 2350 461 750 403 403 750 461 2350 493
3676 452 1036 324 258 258 324 1036 452 3676
493 2350 461 750 403 403 750 461 2350 493
2595 462 1680 607 846 846 607 1680 462 2595
17 992 4185 1517 2609 2049 2049 2609 1517 4185 992
5356 1285 2071 1173 1264 1264 1173 2071 1285 5356
1362 2878 864 906 546 546 906 864 2878 1362
5356 1285 2071 1173 1264 1264 1173 2071 1285 5356
992 4185 1517 2609 2049 2049 2609 1517 4185 992
18 7566 1629 3756 1570 1978 1978 1570 3756 1629 7566
1794 3842 1385 1726 878 878 1726 1385 3842 1794
5574 1464 1912 748 508 508 748 1912 1464 5574
1794 3842 1385 1726 878 878 1726 1385 3842 1794
7566 1629 3756 1570 1978 1978 1570 3756 1629 7566
19 3247 7693 3603 5916 4548 4548 5916 3603 7693 3247
7946 3520 4393 2426 2499 2499 2426 4393 3520 7946
3924 5022 2034 1880 884 884 1880 2034 5022 3924
7946 3520 4393 2426 2499 2499 2426 4393 3520 7946
3247 7693 3603 5916 4548 4548 5916 3603 7693 3247
20 9784 4644 7985 3200 4405 4405 3200 7985 4644 9784
5374 6451 2809 3340 2340 2340 3340 2809 6451 5374
9452 3622 3418 1062 1602 1602 1062 3418 3622 9452
5374 6451 2809 3340 2340 2340 3340 2809 6451 5374
9784 4644 7985 3200 4405 4405 3200 7985 4644 9784
21 8951 12557 7241 10802 9233 9233 10802 7241 12557 8951
13293 7640 6927 4180 5612 5612 4180 6927 7640 13293
9840 8478 3008 3198 2522 2522 3198 3008 8478 9840
13293 7640 6927 4180 5612 5612 4180 6927 7640 13293
8951 12557 7241 10802 9233 9233 10802 7241 12557 8951
22 16931 9839 10312 6748 8302 8302 6748 10312 9839 16931
12400 9393 3607 5665 5498 5498 5665 3607 9393 12400
14238 5862 3326 2664 4874 4874 2664 3326 5862 14238
12400 9393 3607 5665 5498 5498 5665 3607 9393 12400
16931 9839 10312 6748 8302 8302 6748 10312 9839 16931
23 18900 19290 13450 14604 16001 16001 14604 13450 19290 18900
20376 11992 8407 8471 10297 10297 8471 8407 11992 20376
18718 9430 3116 6134 6650 6650 6134 3116 9430 18718
20376 11992 8407 8471 10297 10297 8471 8407 11992 20376
18900 19290 13450 14604 16001 16001 14604 13450 19290 18900
24 23974 15382 14432 12906 8699 8699 12906 14432 15382 23974
18628 7837 6087 6086 9128 9128 6086 6087 7837 18628
16402 4334 4734 6058 10172 10172 6058 4734 4334 16402
18628 7837 6087 6086 9128 9128 6086 6087 7837 18628
23974 15382 14432 12906 8699 8699 12906 14432 15382 23974
25 27486 24067 25217 21433 19449 19449 21433 25217 24067 27486
22447 16303 11589 13930 11949 11949 13930 11589 16303 22447
23112 10424 4000 7824 12462 12462 7824 4000 10424 23112
22447 16303 11589 13930 11949 11949 13930 11589 16303 22447
27486 24067 25217 21433 19449 19449 21433 25217 24067 27486
26 21109 21156 17150 15892 10288 10288 15892 17150 21156 21109
16747 7110 7431 8508 7513 7513 8508 7431 7110 16747
10114 3694 6070 10638 11520 11520 10638 6070 3694 10114
16747 7110 7431 8508 7513 7513 8508 7431 7110 16747
21109 21156 17150 15892 10288 10288 15892 17150 21156 21109
27 28750 28044 31547 26046 20329 20329 26046 31547 28044 28750
20981 15546 13814 15930 14930 14930 15930 13814 15546 20981
25784 8260 5490 11608 13650 13650 11608 5490 8260 25784
20981 15546 13814 15930 14930 14930 15930 13814 15546 20981
28750 28044 31547 26046 20329 20329 26046 31547 28044 28750
28 15530 15930 15393 13958 11959 11959 13958 15393 15930 15530
11891 2870 7062 8101 6442 6442 8101 7062 2870 11891
3938 2432 8166 12678 13058 13058 12678 8166 2432 3938
11891 2870 7062 8101 6442 6442 8101 7062 2870 11891
15530 15930 15393 13958 11959 11959 13958 15393 15930 15530
29 17747 16711 20511 18516 14412 14412 18516 20511 16711 17747
12269 6113 8019 10698 10214 10214 10698 8019 6113 12269
16434 3440 6470 12416 12100 12100 12416 6470 3440 16434
12269 6113 8019 10698 10214 10214 10698 8019 6113 12269
17747 16711 20511 18516 14412 14412 18516 20511 16711 17747
30 6986 5482 3500 4637 7538 7538 4637 3500 5482 6986
3254 415 2886 3656 2891 2891 3656 2886 415 3254
588 2038 7060 9026 5424 5424 9026 7060 2038 588
3254 415 2886 3656 2891 2891 3656 2886 415 3254
6986 5482 3500 4637 7538 7538 4637 3500 5482 6986
31 3042 1587 1201 926 2571 2571 926 1201 1587 3042
686 125 855 522 859 859 522 855 125 686
704 36 4016 2942 848 848 2942 4016 36 704
686 125 855 522 859 859 522 855 125 686
3042 1587 1201 926 2571 2571 926 1201 1587 3042
32 712 399 136 144 522 522 144 136 399 712
51 2 31 42 22 22 42 31 2 51
0 32 1220 522 72 72 522 1220 32 0
51 2 31 42 22 22 42 31 2 51
712 399 136 144 522 522 144 136 399 712
33 26 27 34 0 37 37 0 34 27 26
0 0 2 4 14 14 4 2 0 0
4 0 44 16 22 22 16 44 0 4
0 0 2 4 14 14 4 2 0 0
26 27 34 0 37 37 0 34 27 26
34 0 1 0 0 0 0 0 0 1 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 1 0
Total 215403 191235 180259 162334 144770 144770 162334 180259 191235 215403
176322 104469 89784 96536 94031 94031 96536 89784 104469 176322
165224 74490 67408 91784 98042 98042 91784 67408 74490 165224
176322 104469 89784 96536 94031 94031 96536 89784 104469 176322
215403 191235 180259 162334 144770 144770 162334 180259 191235 215403
Grand total = 2*67408 + 2*74490 + 4*89784 + 2*91784 + 4*94031 + 4*96536 + 2*98042 + 4*104469 + 4*144770 + 4*162334 + 2*165224 + 4*176322 + 4*180259 + 4*191235 + 4*215403
= 6814468
Number of times each node is the end node (EN) in a CNSAP of each length (L)
EN 0 1 2 3 4 5 6 7 8 9
10 11 12 13 14 15 16 17 18 19
20 21 22 23 24 25 26 27 28 29
30 31 32 33 34 35 36 37 38 39
40 41 42 43 44 45 46 47 48 49
L
3 2 0 0 0 0 0 0 0 0 2
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
2 0 0 0 0 0 0 0 0 2
4 4 0 0 0 0 0 0 0 0 4
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
4 0 0 0 0 0 0 0 0 4
5 10 0 0 0 0 0 0 0 0 10
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
10 0 0 0 0 0 0 0 0 10
6 22 0 0 0 0 0 0 0 0 22
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
22 0 0 0 0 0 0 0 0 22
7 46 2 2 2 2 2 2 2 2 46
2 0 0 0 0 0 0 0 0 2
2 0 0 0 0 0 0 0 0 2
2 0 0 0 0 0 0 0 0 2
46 2 2 2 2 2 2 2 2 46
8 83 1 2 2 2 2 2 2 1 83
1 0 0 0 0 0 0 0 0 1
2 0 0 0 0 0 0 0 0 2
1 0 0 0 0 0 0 0 0 1
83 1 2 2 2 2 2 2 1 83
9 159 6 9 10 10 10 10 9 6 159
6 0 0 0 0 0 0 0 0 6
8 0 0 0 0 0 0 0 0 8
6 0 0 0 0 0 0 0 0 6
159 6 9 10 10 10 10 9 6 159
10 282 6 9 13 14 14 13 9 6 282
5 0 0 0 0 0 0 0 0 5
4 0 0 0 0 0 0 0 0 4
5 0 0 0 0 0 0 0 0 5
282 6 9 13 14 14 13 9 6 282
11 536 26 44 49 55 55 49 44 26 536
19 4 8 8 8 8 8 8 4 19
32 8 16 16 16 16 16 16 8 32
19 4 8 8 8 8 8 8 4 19
536 26 44 49 55 55 49 44 26 536
12 987 26 43 58 64 64 58 43 26 987
11 0 4 4 4 4 4 4 0 11
12 4 16 16 16 16 16 16 4 12
11 0 4 4 4 4 4 4 0 11
987 26 43 58 64 64 58 43 26 987
13 1922 100 175 215 230 230 215 175 100 1922
60 20 44 56 56 56 56 44 20 60
88 32 72 96 96 96 96 72 32 88
60 20 44 56 56 56 56 44 20 60
1922 100 175 215 230 230 215 175 100 1922
14 3474 100 176 223 228 228 223 176 100 3474
20 0 32 46 48 48 46 32 0 20
24 16 88 124 128 128 124 88 16 24
20 0 32 46 48 48 46 32 0 20
3474 100 176 223 228 228 223 176 100 3474
15 5866 347 608 785 841 841 785 608 347 5866
175 72 174 278 306 306 278 174 72 175
232 84 240 380 436 436 380 240 84 232
175 72 174 278 306 306 278 174 72 175
5866 347 608 785 841 841 785 608 347 5866
16 9443 381 614 747 765 765 747 614 381 9443
63 0 141 258 304 304 258 141 0 63
44 30 318 564 652 652 564 318 30 44
63 0 141 258 304 304 258 141 0 63
9443 381 614 747 765 765 747 614 381 9443
17 13085 1047 1679 2147 2535 2535 2147 1679 1047 13085
446 177 502 880 1128 1128 880 502 177 446
548 196 726 1228 1608 1608 1228 726 196 548
446 177 502 880 1128 1128 880 502 177 446
13085 1047 1679 2147 2535 2535 2147 1679 1047 13085
18 18452 1171 1776 2099 2274 2274 2099 1776 1171 18452
220 0 444 941 1199 1199 941 444 0 220
104 42 938 1902 2316 2316 1902 938 42 104
220 0 444 941 1199 1199 941 444 0 220
18452 1171 1776 2099 2274 2274 2099 1776 1171 18452
19 21227 2631 4049 5080 5898 5898 5080 4049 2631 21227
1051 357 1233 2322 2999 2999 2322 1233 357 1051
1200 414 1998 3578 4442 4442 3578 1998 414 1200
1051 357 1233 2322 2999 2999 2322 1233 357 1051
21227 2631 4049 5080 5898 5898 5080 4049 2631 21227
20 27619 2705 4389 4985 5395 5395 4985 4389 2705 27619
641 0 1149 2512 3413 3413 2512 1149 0 641
272 76 2536 4978 6342 6342 4978 2536 76 272
641 0 1149 2512 3413 3413 2512 1149 0 641
27619 2705 4389 4985 5395 5395 4985 4389 2705 27619
21 33252 5470 8698 10829 11069 11069 10829 8698 5470 33252
2335 674 2785 5101 6401 6401 5101 2785 674 2335
2560 880 4630 8510 10110 10110 8510 4630 880 2560
2335 674 2785 5101 6401 6401 5101 2785 674 2335
33252 5470 8698 10829 11069 11069 10829 8698 5470 33252
22 39172 4981 8802 10139 10042 10042 10139 8802 4981 39172
1265 0 2441 5218 6769 6769 5218 2441 0 1265
664 190 5792 10548 13502 13502 10548 5792 190 664
1265 0 2441 5218 6769 6769 5218 2441 0 1265
39172 4981 8802 10139 10042 10042 10139 8802 4981 39172
23 43962 9832 16335 18730 17954 17954 18730 16335 9832 43962
4775 1390 5645 8876 10744 10744 8876 5645 1390 4775
5642 1940 9828 15638 18090 18090 15638 9828 1940 5642
4775 1390 5645 8876 10744 10744 8876 5645 1390 4775
43962 9832 16335 18730 17954 17954 18730 16335 9832 43962
24 43831 7531 13844 15448 14476 14476 15448 13844 7531 43831
2345 0 4312 8192 8527 8527 8192 4312 0 2345
1534 486 11270 17696 20020 20020 17696 11270 486 1534
2345 0 4312 8192 8527 8527 8192 4312 0 2345
43831 7531 13844 15448 14476 14476 15448 13844 7531 43831
25 45461 16287 24386 25671 24096 24096 25671 24386 16287 45461
9857 3130 9263 13513 12327 12327 13513 9263 3130 9857
12548 4366 15984 22772 21910 21910 22772 15984 4366 12548
9857 3130 9263 13513 12327 12327 13513 9263 3130 9857
45461 16287 24386 25671 24096 24096 25671 24386 16287 45461
26 35276 9550 15272 17642 17180 17180 17642 15272 9550 35276
4060 0 6127 9472 8200 8200 9472 6127 0 4060
3204 1162 16538 23120 18262 18262 23120 16538 1162 3204
4060 0 6127 9472 8200 8200 9472 6127 0 4060
35276 9550 15272 17642 17180 17180 17642 15272 9550 35276
27 39225 21388 27719 27241 26845 26845 27241 27719 21388 39225
15011 5180 11397 14730 14077 14077 14730 11397 5180 15011
19318 6976 20012 24686 20008 20008 24686 20012 6976 19318
15011 5180 11397 14730 14077 14077 14730 11397 5180 15011
39225 21388 27719 27241 26845 26845 27241 27719 21388 39225
28 23337 8517 11876 14078 16617 16617 14078 11876 8517 23337
5065 0 6123 7903 7087 7087 7903 6123 0 5065
3242 2048 18454 20074 13520 13520 20074 18454 2048 3242
5065 0 6123 7903 7087 7087 7903 6123 0 5065
23337 8517 11876 14078 16617 16617 14078 11876 8517 23337
29 22023 14851 17072 16615 18110 18110 16615 17072 14851 22023
10381 3839 7568 9784 9423 9423 9784 7568 3839 10381
12492 4306 15530 16586 13034 13034 16586 15530 4306 12492
10381 3839 7568 9784 9423 9423 9784 7568 3839 10381
22023 14851 17072 16615 18110 18110 16615 17072 14851 22023
30 9183 4244 3393 4684 8280 8280 4684 3393 4244 9183
1875 0 2564 3127 2676 2676 3127 2564 0 1875
464 1580 11264 8678 4588 4588 8678 11264 1580 464
1875 0 2564 3127 2676 2676 3127 2564 0 1875
9183 4244 3393 4684 8280 8280 4684 3393 4244 9183
31 3380 1453 1212 1002 2723 2723 1002 1212 1453 3380
404 54 642 458 696 696 458 642 54 404
664 68 4964 2634 916 916 2634 4964 68 664
404 54 642 458 696 696 458 642 54 404
3380 1453 1212 1002 2723 2723 1002 1212 1453 3380
32 712 375 170 142 510 510 142 170 375 712
43 0 29 44 32 32 44 29 0 43
4 32 1248 476 94 94 476 1248 32 4
43 0 29 44 32 32 44 29 0 43
712 375 170 142 510 510 142 170 375 712
33 25 28 34 0 37 37 0 34 28 25
0 0 2 4 14 14 4 2 0 0
4 0 44 16 22 22 16 44 0 4
0 0 2 4 14 14 4 2 0 0
25 28 34 0 37 37 0 34 28 25
34 0 1 0 0 0 0 0 0 1 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 1 0
Total 442058 113057 162388 178636 186252 186252 178636 162388 113057 442058
60136 14897 62629 93727 96438 96438 93727 62629 14897 60136
64912 24936 142506 184316 170128 170128 184316 142506 24936 64912
60136 14897 62629 93727 96438 96438 93727 62629 14897 60136
442058 113057 162388 178636 186252 186252 178636 162388 113057 442058
Grand total = 4*14897 + 2*24936 + 4*60136 + 4*62629 + 2*64912 + 4*93727 + 4*96438 + 4*113057 + 2*142506 + 4*162388 + 2*170128 + 4*178636 + 2*184316 + 4*186252 + 4*442058
= 6814468
Number of times each node (N) is present in a CNSAP of each length (L)
N 0 1 2 3 4 5 6 7 8 9
10 11 12 13 14 15 16 17 18 19
20 21 22 23 24 25 26 27 28 29
30 31 32 33 34 35 36 37 38 39
40 41 42 43 44 45 46 47 48 49
L
3 2 1 0 0 0 0 0 0 1 2
1 2 0 0 0 0 0 0 2 1
0 0 0 0 0 0 0 0 0 0
1 2 0 0 0 0 0 0 2 1
2 1 0 0 0 0 0 0 1 2
4 4 2 0 0 0 0 0 0 2 4
2 4 2 0 0 0 0 2 4 2
0 4 0 0 0 0 0 0 4 0
2 4 2 0 0 0 0 2 4 2
4 2 0 0 0 0 0 0 2 4
5 10 5 1 0 0 0 0 1 5 10
5 12 5 2 0 0 2 5 12 5
2 10 8 0 0 0 0 8 10 2
5 12 5 2 0 0 2 5 12 5
10 5 1 0 0 0 0 1 5 10
6 22 13 1 3 0 0 3 1 13 22
14 28 17 6 2 2 6 17 28 14
2 22 16 12 0 0 12 16 22 2
14 28 17 6 2 2 6 17 28 14
22 13 1 3 0 0 3 1 13 22
7 53 32 17 7 9 9 7 17 32 53
31 60 47 30 12 12 30 47 60 31
14 58 62 40 28 28 40 62 58 14
31 60 47 30 12 12 30 47 60 31
53 32 17 7 9 9 7 17 32 53
8 86 54 20 31 17 17 31 20 54 86
50 101 87 64 51 51 64 87 101 50
10 78 106 84 72 72 84 106 78 10
50 101 87 64 51 51 64 87 101 50
86 54 20 31 17 17 31 20 54 86
9 183 113 61 78 95 95 78 61 113 183
113 206 185 161 176 176 161 185 206 113
44 166 240 250 230 230 250 240 166 44
113 206 185 161 176 176 161 185 206 113
183 113 61 78 95 95 78 61 113 183
10 308 191 88 123 239 239 123 88 191 308
178 348 297 342 383 383 342 297 348 178
34 266 376 436 514 514 436 376 266 34
178 348 297 342 383 383 342 297 348 178
308 191 88 123 239 239 123 88 191 308
11 630 452 317 532 553 553 532 317 452 630
440 811 873 993 1058 1058 993 873 811 440
220 662 868 1252 1302 1302 1252 868 662 220
440 811 873 993 1058 1058 993 873 811 440
630 452 317 532 553 553 532 317 452 630
12 1096 712 640 805 941 941 805 640 712 1096
661 1457 1403 1700 1798 1798 1700 1403 1457 661
200 1098 1658 1952 2258 2258 1952 1658 1098 200
661 1457 1403 1700 1798 1798 1700 1403 1457 661
1096 712 640 805 941 941 805 640 712 1096
13 2336 2232 1967 2612 2820 2820 2612 1967 2232 2336
1902 3482 3957 4427 4831 4831 4427 3957 3482 1902
1014 3174 3976 5040 5484 5484 5040 3976 3174 1014
1902 3482 3957 4427 4831 4831 4427 3957 3482 1902
2336 2232 1967 2612 2820 2820 2612 1967 2232 2336
14 4408 3219 2989 3793 4438 4438 3793 2989 3219 4408
2764 6375 6290 6882 7258 7258 6882 6290 6375 2764
1584 5350 7396 7856 8018 8018 7856 7396 5350 1584
2764 6375 6290 6882 7258 7258 6882 6290 6375 2764
4408 3219 2989 3793 4438 4438 3793 2989 3219 4408
15 7746 8357 8563 11483 13106 13106 11483 8563 8357 7746
7653 13337 14515 15653 17585 17585 15653 14515 13337 7653
4840 13640 15686 16492 17486 17486 16492 15686 13640 4840
7653 13337 14515 15653 17585 17585 15653 14515 13337 7653
7746 8357 8563 11483 13106 13106 11483 8563 8357 7746
16 13743 11246 11637 14987 17535 17535 14987 11637 11246 13743
10322 21553 21213 21996 22289 22289 21996 21213 21553 10322
8510 21082 24540 23550 21916 21916 23550 24540 21082 8510
10322 21553 21213 21996 22289 22289 21996 21213 21553 10322
13743 11246 11637 14987 17535 17535 14987 11637 11246 13743
17 20029 24850 28057 37318 43100 43100 37318 28057 24850 20029
23149 38307 40849 42949 45546 45546 42949 40849 38307 23149
19298 40928 43754 42338 41860 41860 42338 43754 40928 19298
23149 38307 40849 42949 45546 45546 42949 40849 38307 23149
20029 24850 28057 37318 43100 43100 37318 28057 24850 20029
18 33216 32601 36112 44302 49622 49622 44302 36112 32601 33216
30365 54500 53303 53746 52571 52571 53746 53303 54500 30365
27212 55168 58258 53804 49054 49054 53804 58258 55168 27212
30365 54500 53303 53746 52571 52571 53746 53303 54500 30365
33216 32601 36112 44302 49622 49622 44302 36112 32601 33216
19 43958 60784 73446 92925 99577 99577 92925 73446 60784 43958
56385 86833 93148 97985 92825 92825 97985 93148 86833 56385
55772 90776 91814 90298 76802 76802 90298 91814 90776 55772
56385 86833 93148 97985 92825 92825 97985 93148 86833 56385
43958 60784 73446 92925 99577 99577 92925 73446 60784 43958
20 61909 77912 92383 103254 108208 108208 103254 92383 77912 61909
72694 113045 110238 108159 105788 105788 108159 110238 113045 72694
73802 113262 109310 99104 93742 93742 99104 109310 113262 73802
72694 113045 110238 108159 105788 105788 108159 110238 113045 72694
61909 77912 92383 103254 108208 108208 103254 92383 77912 61909
21 93027 140279 176579 200816 207859 207859 200816 176579 140279 93027
130966 186938 196443 182289 179349 179349 182289 196443 186938 130966
141362 193746 185142 151008 137930 137930 151008 185142 193746 141362
130966 186938 196443 182289 179349 179349 182289 196443 186938 130966
93027 140279 176579 200816 207859 207859 200816 176579 140279 93027
22 118758 166143 195885 210609 212324 212324 210609 195885 166143 118758
158576 213513 196273 187840 188691 188691 187840 196273 213513 158576
171098 215512 180956 157756 161242 161242 157756 180956 215512 171098
158576 213513 196273 187840 188691 188691 187840 196273 213513 158576
118758 166143 195885 210609 212324 212324 210609 195885 166143 118758
23 176621 279891 342221 367633 369993 369993 367633 342221 279891 176621
268483 349571 319767 301027 305496 305496 301027 319767 349571 268483
307864 361136 267284 219046 218616 218616 219046 267284 361136 307864
268483 349571 319767 301027 305496 305496 301027 319767 349571 268483
176621 279891 342221 367633 369993 369993 367633 342221 279891 176621
24 187247 271818 316254 330161 322521 322521 330161 316254 271818 187247
276455 315074 272210 261082 268090 268090 261082 272210 315074 276455
312036 311802 223204 200948 222618 222618 200948 223204 311802 312036
276455 315074 272210 261082 268090 268090 261082 272210 315074 276455
187247 271818 316254 330161 322521 322521 330161 316254 271818 187247
25 284986 453357 547089 554442 522561 522561 554442 547089 453357 284986
469263 504874 428798 420657 433249 433249 420657 428798 504874 469263
561356 494298 290642 257686 296516 296516 257686 290642 494298 561356
469263 504874 428798 420657 433249 433249 420657 428798 504874 469263
284986 453357 547089 554442 522561 522561 554442 547089 453357 284986
26 232646 350122 398595 388058 352918 352918 388058 398595 350122 232646
368149 344626 286514 287763 294597 294597 287763 286514 344626 368149
426352 316514 195158 209684 248260 248260 209684 195158 316514 426352
368149 344626 286514 287763 294597 294597 287763 286514 344626 368149
232646 350122 398595 388058 352918 352918 388058 398595 350122 232646
27 401037 609605 714779 661126 573365 573365 661126 714779 609605 401037
668866 533616 467204 486086 507718 507718 486086 467204 533616 668866
809658 456952 252292 287566 355630 355630 287566 252292 456952 809658
668866 533616 467204 486086 507718 507718 486086 467204 533616 668866
401037 609605 714779 661126 573365 573365 661126 714779 609605 401037
28 243676 348804 391206 347482 298954 298954 347482 391206 348804 243676
379866 261660 234267 246107 252479 252479 246107 234267 261660 379866
444920 221446 145892 190630 227342 227342 190630 145892 221446 444920
379866 261660 234267 246107 252479 252479 246107 234267 261660 379866
243676 348804 391206 347482 298954 298954 347482 391206 348804 243676
29 330477 481012 551603 459111 364424 364424 459111 551603 481012 330477
504053 294117 277042 311117 322809 322809 311117 277042 294117 504053
606966 235890 140128 234230 308376 308376 234230 140128 235890 606966
504053 294117 277042 311117 322809 322809 311117 277042 294117 504053
330477 481012 551603 459111 364424 364424 459111 551603 481012 330477
30 123097 169937 186268 152225 127928 127928 152225 186268 169937 123097
173323 90108 91191 104066 106301 106301 104066 91191 90108 173323
203466 77584 63480 97176 108186 108186 97176 63480 77584 203466
173323 90108 91191 104066 106301 106301 104066 91191 90108 173323
123097 169937 186268 152225 127928 127928 152225 186268 169937 123097
31 42229 56233 60200 44917 46286 46286 44917 60200 56233 42229
55833 25185 29857 29386 33713 33713 29386 29857 25185 55833
65020 19896 28276 37260 33984 33984 37260 28276 19896 65020
55833 25185 29857 29386 33713 33713 29386 29857 25185 55833
42229 56233 60200 44917 46286 46286 44917 60200 56233 42229
32 8669 10896 10794 7810 9103 9103 7810 10794 10896 8669
10506 3571 5202 4946 5900 5900 4946 5202 3571 10506
11760 2912 7424 7884 6202 6202 7884 7424 2912 11760
10506 3571 5202 4946 5900 5900 4946 5202 3571 10506
8669 10896 10794 7810 9103 9103 7810 10794 10896 8669
33 592 729 666 338 712 712 338 666 729 592
696 182 408 264 372 372 264 408 182 696
748 96 568 564 448 448 564 568 96 748
696 182 408 264 372 372 264 408 182 696
592 729 666 338 712 712 338 666 729 592
34 4 4 2 2 4 4 2 2 4 4
4 0 4 2 2 2 2 4 0 4
4 0 4 0 4 4 0 4 0 4
4 0 4 2 2 2 2 4 0 4
4 4 2 2 4 4 2 2 4 4
Total 2432805 3561606 4148440 4036983 3749212 3749212 4036983 4148440 3561606 2432805
3671768 3463496 3151609 3177727 3250939 3250939 3177727 3151609 3463496 3671768
4255168 3253528 2338518 2393946 2644120 2644120 2393946 2338518 3253528 4255168
3671768 3463496 3151609 3177727 3250939 3250939 3177727 3151609 3463496 3671768
2432805 3561606 4148440 4036983 3749212 3749212 4036983 4148440 3561606 2432805
Grand total = 2*2338518 + 2*2393946 + 4*2432805 + 2*2644120 + 4*3151609 + 4*3177727 + 4*3250939 + 2*3253528 + 4*3463496 + 4*3561606 + 4*3671768 + 4*3749212 + 4*4036983 + 4*4148440 + 2*4255168
= 168348900
Number of CNSAPs for each start node (SN) and end node (EN) pair
SN 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45 46 47 48 49
EN
0 0 0 20266 15847 13720 10628 10506 11857 12901 14462 0 2 4537 9820 10202 7811 6191 5886 6804 11367 19948 2756 2064 5649 7232 7593 7288 5662 5225 10630 16287 7519 4224 3102 3634 6323 8154
7879 7741 12245 16085 11289 7658 6046 6925 10316 13415 15045 14994 16323
1 0 0 0 15410 581 867 1000 2943 3538 3704 15160 0 7407 4636 3 29 567 1440 1837 2766 0 0 2610 1528 1695 2576 1734 1158 1154 2383 0 0 0 922 2709 2769 1935
1300 1398 2521 1114 1114 1114 2066 3275 2958 2738 2569 2653 3176
2 15301 0 0 0 15920 494 1814 2194 3970 4466 5105 12021 0 11485 4782 20 114 1168 2176 3596 0 0 1556 4352 1460 2860 3520 1962 1614 3436 389 0 0 0 2010 5692 4428
2694 2338 4080 778 778 778 1556 4325 6526 5540 4966 4690 5434
3 8249 16444 0 0 0 14095 681 2271 2583 3519 2004 1720 8530 0 11487 4339 198 435 1658 3328 2004 0 1718 3004 4395 1326 3116 2669 1824 3694 2146 934 0 0 0 3366 6861
4532 3210 4950 2146 2580 1628 1134 2696 6894 9029 7558 6587 7094
4 4201 3545 15990 0 0 0 14298 1528 2493 2770 3109 901 3514 8113 0 9467 4246 472 1155 2983 3280 1361 872 3262 3472 3927 1343 2139 1980 3596 3838 3151 2037 0 0 0 3280
5243 3804 4813 5003 5931 5659 3037 1828 3592 7643 9063 7200 7113
5 2770 2493 1528 14298 0 0 0 15990 3545 4201 2983 1155 472 4246 9467 0 8113 3514 901 3109 3596 1980 2139 1343 3927 3472 3262 872 1361 3280 4813 3804 5243 3280 0 0 0
2037 3151 3838 7113 7200 9063 7643 3592 1828 3037 5659 5931 5003
6 3519 2583 2271 681 14095 0 0 0 16444 8249 3328 1658 435 198 4339 11487 0 8530 1720 2004 3694 1824 2669 3116 1326 4395 3004 1718 0 2004 4950 3210 4532 6861 3366 0 0
0 934 2146 7094 6587 7558 9029 6894 2696 1134 1628 2580 2146
7 4466 3970 2194 1814 494 15920 0 0 0 15301 3596 2176 1168 114 20 4782 11485 0 12021 5105 3436 1614 1962 3520 2860 1460 4352 1556 0 0 4080 2338 2694 4428 5692 2010 0
0 0 389 5434 4690 4966 5540 6526 4325 1556 778 778 778
8 3704 3538 2943 1000 867 581 15410 0 0 0 2766 1837 1440 567 29 3 4636 7407 0 15160 2383 1154 1158 1734 2576 1695 1528 2610 0 0 2521 1398 1300 1935 2769 2709 922
0 0 0 3176 2653 2569 2738 2958 3275 2066 1114 1114 1114
9 14462 12901 11857 10506 10628 13720 15847 20266 0 0 11367 6804 5886 6191 7811 10202 9820 4537 2 0 10630 5225 5662 7288 7593 7232 5649 2064 2756 19948 12245 7741 7879 8154 6323 3634 3102
4224 7519 16287 16323 14994 15045 13415 10316 6925 6046 7658 11289 16085
10 0 15160 0 0 575 588 518 515 571 677 0 0 0 0 550 491 331 252 306 551 0 6776 910 295 391 291 320 281 271 547 14329 794 0 1 3 6 344
467 449 663 6581 794 603 214 72 249 698 911 879 912
11 0 0 6916 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7981 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
12 5142 5558 0 5660 1628 726 680 835 1135 1299 5142 0 0 0 2724 19 403 361 623 1079 2654 4384 0 1431 926 221 871 650 532 1082 0 0 0 0 0 1158 1750
1091 826 1334 0 0 0 0 852 2208 2244 1901 1660 1840
13 5130 4840 7989 0 5405 2852 1480 1550 1606 1958 2710 3918 0 0 0 4952 114 810 922 1814 922 922 2098 0 2640 1558 414 1164 1092 2092 922 0 0 0 0 0 2440
2934 2024 2768 922 569 0 0 0 2178 5136 4866 3980 4036
14 3508 2488 3788 7968 0 6468 3078 1657 2038 2285 2264 1020 4608 0 0 0 5540 381 1105 2017 1688 352 1248 1836 0 2504 1784 434 1122 2302 2040 1056 0 0 0 0 0
2010 2512 2930 2392 2568 1320 0 0 0 2349 5062 4530 4186
15 2285 2038 1657 3078 6468 0 7968 3788 2488 3508 2017 1105 381 5540 0 0 0 4608 1020 2264 2302 1122 434 1784 2504 0 1836 1248 352 1688 2930 2512 2010 0 0 0 0
0 1056 2040 4186 4530 5062 2349 0 0 0 1320 2568 2392
16 1958 1606 1550 1480 2852 5405 0 7989 4840 5130 1814 922 810 114 4952 0 0 0 3918 2710 2092 1092 1164 414 1558 2640 0 2098 922 922 2768 2024 2934 2440 0 0 0
0 0 922 4036 3980 4866 5136 2178 0 0 0 569 922
17 1299 1135 835 680 726 1628 5660 0 5558 5142 1079 623 361 403 19 2724 0 0 0 5142 1082 532 650 871 221 926 1431 0 4384 2654 1334 826 1091 1750 1158 0 0
0 0 0 1840 1660 1901 2244 2208 852 0 0 0 0
18 0 0 0 0 0 0 0 6916 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7981 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
19 677 571 515 518 588 575 0 0 15160 0 551 306 252 331 491 550 0 0 0 0 547 271 281 320 291 391 295 910 6776 0 663 449 467 344 6 3 1
0 794 14329 912 879 911 698 249 72 214 603 794 6581
20 14901 4787 0 0 0 0 0 0 0 0 0 12768 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 12768 0 0 0 0 0
0 0 0 14901 4787 0 0 0 0 0 0 0 0
21 1844 1844 989 0 0 0 0 0 0 0 5072 0 2719 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5072 0 2719 0 0 0 0
0 0 0 1844 1844 989 0 0 0 0 0 0 0
22 4650 5676 3638 2082 1404 2580 3980 4432 4500 4956 5745 3296 0 1850 944 1240 2296 2256 2344 3792 6840 0 0 0 2288 1176 2016 1760 1688 3416 5745 3296 0 1850 944 1240 2296
2256 2344 3792 4650 5676 3638 2082 1404 2580 3980 4432 4500 4956
23 6224 4672 5780 3706 2928 2165 4287 6744 6808 7380 4466 3120 3721 0 2234 1663 1677 3390 3553 5641 4276 3516 0 0 0 4444 1686 2446 2532 5098 4466 3120 3721 0 2234 1663 1677
3390 3553 5641 6224 4672 5780 3706 2928 2165 4287 6744 6808 7380
24 6514 4710 3188 4092 2972 3280 2402 4488 6572 7128 4920 2028 1952 4010 0 3404 1728 1534 3436 5436 4228 1632 3360 0 0 0 4588 1452 2392 4888 4920 2028 1952 4010 0 3404 1728
1534 3436 5436 6514 4710 3188 4092 2972 3280 2402 4488 6572 7128
25 7128 6572 4488 2402 3280 2972 4092 3188 4710 6514 5436 3436 1534 1728 3404 0 4010 1952 2028 4920 4888 2392 1452 4588 0 0 0 3360 1632 4228 5436 3436 1534 1728 3404 0 4010
1952 2028 4920 7128 6572 4488 2402 3280 2972 4092 3188 4710 6514
26 7380 6808 6744 4287 2165 2928 3706 5780 4672 6224 5641 3553 3390 1677 1663 2234 0 3721 3120 4466 5098 2532 2446 1686 4444 0 0 0 3516 4276 5641 3553 3390 1677 1663 2234 0
3721 3120 4466 7380 6808 6744 4287 2165 2928 3706 5780 4672 6224
27 4956 4500 4432 3980 2580 1404 2082 3638 5676 4650 3792 2344 2256 2296 1240 944 1850 0 3296 5745 3416 1688 1760 2016 1176 2288 0 0 0 6840 3792 2344 2256 2296 1240 944 1850
0 3296 5745 4956 4500 4432 3980 2580 1404 2082 3638 5676 4650
28 0 0 0 0 0 0 0 989 1844 1844 0 0 0 0 0 0 0 2719 0 5072 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2719 0 5072 0 0 0 0 0 0 0 989 1844 1844
29 0 0 0 0 0 0 0 0 4787 14901 0 0 0 0 0 0 0 0 12768 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 12768 0 0 0 0 0 0 0 0 0 4787 14901
30 6581 794 603 214 72 249 698 911 879 912 14329 794 0 1 3 6 344 467 449 663 0 6776 910 295 391 291 320 281 271 547 0 0 0 0 550 491 331
252 306 551 0 15160 0 0 575 588 518 515 571 677
31 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7981 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 6916 0 0 0 0 0 0 0
32 0 0 0 0 852 2208 2244 1901 1660 1840 0 0 0 0 0 1158 1750 1091 826 1334 2654 4384 0 1431 926 221 871 650 532 1082 5142 0 0 0 2724 19 403
361 623 1079 5142 5558 0 5660 1628 726 680 835 1135 1299
33 922 569 0 0 0 2178 5136 4866 3980 4036 922 0 0 0 0 0 2440 2934 2024 2768 922 922 2098 0 2640 1558 414 1164 1092 2092 2710 3918 0 0 0 4952 114
810 922 1814 5130 4840 7989 0 5405 2852 1480 1550 1606 1958
34 2392 2568 1320 0 0 0 2349 5062 4530 4186 2040 1056 0 0 0 0 0 2010 2512 2930 1688 352 1248 1836 0 2504 1784 434 1122 2302 2264 1020 4608 0 0 0 5540
381 1105 2017 3508 2488 3788 7968 0 6468 3078 1657 2038 2285
35 4186 4530 5062 2349 0 0 0 1320 2568 2392 2930 2512 2010 0 0 0 0 0 1056 2040 2302 1122 434 1784 2504 0 1836 1248 352 1688 2017 1105 381 5540 0 0 0
4608 1020 2264 2285 2038 1657 3078 6468 0 7968 3788 2488 3508
36 4036 3980 4866 5136 2178 0 0 0 569 922 2768 2024 2934 2440 0 0 0 0 0 922 2092 1092 1164 414 1558 2640 0 2098 922 922 1814 922 810 114 4952 0 0
0 3918 2710 1958 1606 1550 1480 2852 5405 0 7989 4840 5130
37 1840 1660 1901 2244 2208 852 0 0 0 0 1334 826 1091 1750 1158 0 0 0 0 0 1082 532 650 871 221 926 1431 0 4384 2654 1079 623 361 403 19 2724 0
0 0 5142 1299 1135 835 680 726 1628 5660 0 5558 5142
38 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7981 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 6916 0 0
39 912 879 911 698 249 72 214 603 794 6581 663 449 467 344 6 3 1 0 794 14329 547 271 281 320 291 391 295 910 6776 0 551 306 252 331 491 550 0
0 0 0 677 571 515 518 588 575 0 0 15160 0
40 16085 11289 7658 6046 6925 10316 13415 15045 14994 16323 16287 7519 4224 3102 3634 6323 8154 7879 7741 12245 19948 2756 2064 5649 7232 7593 7288 5662 5225 10630 0 2 4537 9820 10202 7811 6191
5886 6804 11367 0 0 20266 15847 13720 10628 10506 11857 12901 14462
41 1114 1114 1114 2066 3275 2958 2738 2569 2653 3176 0 0 0 922 2709 2769 1935 1300 1398 2521 0 0 2610 1528 1695 2576 1734 1158 1154 2383 15160 0 7407 4636 3 29 567
1440 1837 2766 0 0 0 15410 581 867 1000 2943 3538 3704
42 778 778 778 1556 4325 6526 5540 4966 4690 5434 389 0 0 0 2010 5692 4428 2694 2338 4080 0 0 1556 4352 1460 2860 3520 1962 1614 3436 5105 12021 0 11485 4782 20 114
1168 2176 3596 15301 0 0 0 15920 494 1814 2194 3970 4466
43 2146 2580 1628 1134 2696 6894 9029 7558 6587 7094 2146 934 0 0 0 3366 6861 4532 3210 4950 2004 0 1718 3004 4395 1326 3116 2669 1824 3694 2004 1720 8530 0 11487 4339 198
435 1658 3328 8249 16444 0 0 0 14095 681 2271 2583 3519
44 5003 5931 5659 3037 1828 3592 7643 9063 7200 7113 3838 3151 2037 0 0 0 3280 5243 3804 4813 3280 1361 872 3262 3472 3927 1343 2139 1980 3596 3109 901 3514 8113 0 9467 4246
472 1155 2983 4201 3545 15990 0 0 0 14298 1528 2493 2770
45 7113 7200 9063 7643 3592 1828 3037 5659 5931 5003 4813 3804 5243 3280 0 0 0 2037 3151 3838 3596 1980 2139 1343 3927 3472 3262 872 1361 3280 2983 1155 472 4246 9467 0 8113
3514 901 3109 2770 2493 1528 14298 0 0 0 15990 3545 4201
46 7094 6587 7558 9029 6894 2696 1134 1628 2580 2146 4950 3210 4532 6861 3366 0 0 0 934 2146 3694 1824 2669 3116 1326 4395 3004 1718 0 2004 3328 1658 435 198 4339 11487 0
8530 1720 2004 3519 2583 2271 681 14095 0 0 0 16444 8249
47 5434 4690 4966 5540 6526 4325 1556 778 778 778 4080 2338 2694 4428 5692 2010 0 0 0 389 3436 1614 1962 3520 2860 1460 4352 1556 0 0 3596 2176 1168 114 20 4782 11485
0 12021 5105 4466 3970 2194 1814 494 15920 0 0 0 15301
48 3176 2653 2569 2738 2958 3275 2066 1114 1114 1114 2521 1398 1300 1935 2769 2709 922 0 0 0 2383 1154 1158 1734 2576 1695 1528 2610 0 0 2766 1837 1440 567 29 3 4636
7407 0 15160 3704 3538 2943 1000 867 581 15410 0 0 0
49 16323 14994 15045 13415 10316 6925 6046 7658 11289 16085 12245 7741 7879 8154 6323 3634 3102 4224 7519 16287 10630 5225 5662 7288 7593 7232 5649 2064 2756 19948 11367 6804 5886 6191 7811 10202 9820
4537 2 0 14462 12901 11857 10506 10628 13720 15847 20266 0 0
Sum of all rows = 4(3*0 + 1*2 + 1*2064 + 1*2756 + 1*3102 + 1*3634 + 1*4224 + 1*4537 + 1*5225 + 1*5649 + 1*5662 + 1*5886 + 1*6046 + 1*6191 + 1*6323 + 1*6804 + 1*6925 + 1*7232 + 1*7288 + 1*7519 + 1*7593 + 1*7658 +
1*7741 + 1*7811 + 1*7879 + 1*8154 + 1*9820 + 1*10202 + 1*10316 + 1*10506 + 1*10628 + 1*10630 + 1*11289 + 1*11367 + 1*11857 + 1*12245 + 1*12901 + 1*13415 + 1*13720 + 1*14462 + 1*14994 +
1*15045 + 1*15847 + 1*16085 + 1*16287 + 1*16323 + 1*19948 + 1*20266) +
4(9*0 + 1*3 + 1*29 + 1*567 + 1*581 + 1*867 + 1*922 + 1*1000 + 3*1114 + 1*1154 + 1*1158 + 1*1300 + 1*1398 + 1*1440 + 1*1528 + 1*1695 + 1*1734 + 1*1837 + 1*1935 + 1*2066 + 1*2383 + 1*2521 +
1*2569 + 1*2576 + 1*2610 + 1*2653 + 1*2709 + 1*2738 + 1*2766 + 1*2769 + 1*2943 + 1*2958 + 1*3176 + 1*3275 + 1*3538 + 1*3704 + 1*4636 + 1*7407 + 1*15160 + 1*15410) +
4(9*0 + 1*20 + 1*114 + 1*389 + 1*494 + 3*778 + 1*1168 + 1*1460 + 2*1556 + 1*1614 + 1*1814 + 1*1962 + 1*2010 + 1*2176 + 1*2194 + 1*2338 + 1*2694 + 1*2860 + 1*3436 + 1*3520 + 1*3596 + 1*3970 +
1*4080 + 1*4325 + 1*4352 + 1*4428 + 1*4466 + 1*4690 + 1*4782 + 1*4966 + 1*5105 + 1*5434 + 1*5540 + 1*5692 + 1*6526 + 1*11485 + 1*12021 + 1*15301 + 1*15920) +
4(8*0 + 1*198 + 1*435 + 1*681 + 1*934 + 1*1134 + 1*1326 + 1*1628 + 1*1658 + 1*1718 + 1*1720 + 1*1824 + 2*2004 + 2*2146 + 1*2271 + 1*2580 + 1*2583 + 1*2669 + 1*2696 + 1*3004 + 1*3116 + 1*3210 +
1*3328 + 1*3366 + 1*3519 + 1*3694 + 1*4339 + 1*4395 + 1*4532 + 1*4950 + 1*6587 + 1*6861 + 1*6894 + 1*7094 + 1*7558 + 1*8249 + 1*8530 + 1*9029 + 1*11487 + 1*14095 + 1*16444) +
4(7*0 + 1*472 + 1*872 + 1*901 + 1*1155 + 1*1343 + 1*1361 + 1*1528 + 1*1828 + 1*1980 + 1*2037 + 1*2139 + 1*2493 + 1*2770 + 1*2983 + 1*3037 + 1*3109 + 1*3151 + 1*3262 + 2*3280 + 1*3472 + 1*3514 +
1*3545 + 1*3592 + 1*3596 + 1*3804 + 1*3838 + 1*3927 + 1*4201 + 1*4246 + 1*4813 + 1*5003 + 1*5243 + 1*5659 + 1*5931 + 1*7113 + 1*7200 + 1*7643 + 1*8113 + 1*9063 + 1*9467 + 1*14298 + 1*15990) +
4(9*0 + 1*1 + 1*3 + 1*6 + 1*72 + 1*214 + 1*249 + 1*252 + 1*271 + 1*281 + 1*291 + 1*295 + 1*306 + 1*320 + 1*331 + 1*344 + 1*391 + 1*449 + 1*467 + 1*491 + 1*515 + 1*518 + 1*547 + 1*550 + 1*551 +
1*571 + 1*575 + 1*588 + 1*603 + 1*663 + 1*677 + 1*698 + 2*794 + 1*879 + 1*910 + 1*911 + 1*912 + 1*6581 + 1*6776 + 1*14329 + 1*15160) +
4(48*0 + 1*6916 + 1*7981) +
4(14*0 + 1*19 + 1*221 + 1*361 + 1*403 + 1*532 + 1*623 + 1*650 + 1*680 + 1*726 + 1*826 + 1*835 + 1*852 + 1*871 + 1*926 + 1*1079 + 1*1082 + 1*1091 + 1*1135 + 1*1158 + 1*1299 + 1*1334 + 1*1431 +
1*1628 + 1*1660 + 1*1750 + 1*1840 + 1*1901 + 1*2208 + 1*2244 + 1*2654 + 1*2724 + 1*4384 + 2*5142 + 1*5558 + 1*5660) +
4(13*0 + 1*114 + 1*414 + 1*569 + 1*810 + 5*922 + 1*1092 + 1*1164 + 1*1480 + 1*1550 + 1*1558 + 1*1606 + 1*1814 + 1*1958 + 1*2024 + 1*2092 + 1*2098 + 1*2178 + 1*2440 + 1*2640 + 1*2710 + 1*2768 +
1*2852 + 1*2934 + 1*3918 + 1*3980 + 1*4036 + 1*4840 + 1*4866 + 1*4952 + 1*5130 + 1*5136 + 1*5405 + 1*7989) +
4(13*0 + 1*352 + 1*381 + 1*434 + 1*1020 + 1*1056 + 1*1105 + 1*1122 + 1*1248 + 1*1320 + 1*1657 + 1*1688 + 1*1784 + 1*1836 + 1*2010 + 1*2017 + 1*2038 + 1*2040 + 1*2264 + 1*2285 + 1*2302 + 1*2349 +
1*2392 + 1*2488 + 1*2504 + 1*2512 + 1*2568 + 1*2930 + 1*3078 + 1*3508 + 1*3788 + 1*4186 + 1*4530 + 1*4608 + 1*5062 + 1*5540 + 1*6468 + 1*7968) +
2(44*0 + 2*4787 + 2*12768 + 2*14901) +
2(40*0 + 2*989 + 4*1844 + 2*2719 + 2*5072) +
2(5*0 + 2*944 + 1*1176 + 2*1240 + 2*1404 + 1*1688 + 1*1760 + 2*1850 + 1*2016 + 2*2082 + 2*2256 + 1*2288 + 2*2296 + 2*2344 + 2*2580 + 2*3296 + 1*3416 + 2*3638 + 2*3792 + 2*3980 + 2*4432 +
2*4500 + 2*4650 + 2*4956 + 2*5676 + 2*5745 + 1*6840) +
2(5*0 + 2*1663 + 2*1677 + 1*1686 + 2*2165 + 2*2234 + 1*2446 + 1*2532 + 2*2928 + 2*3120 + 2*3390 + 1*3516 + 2*3553 + 2*3706 + 2*3721 + 1*4276 + 2*4287 + 1*4444 + 2*4466 + 2*4672 + 1*5098 +
2*5641 + 2*5780 + 2*6224 + 2*6744 + 2*6808 + 2*7380) +
2(5*0 + 1*1452 + 2*1534 + 1*1632 + 2*1728 + 2*1952 + 2*2028 + 1*2392 + 2*2402 + 2*2972 + 2*3188 + 2*3280 + 1*3360 + 2*3404 + 2*3436 + 2*4010 + 2*4092 + 1*4228 + 2*4488 + 1*4588 + 2*4710 +
1*4888 + 2*4920 + 2*5436 + 2*6514 + 2*6572 + 2*7128)
= 1768232 + 452228 + 649552 + 714544 + 745008 + 240544 + 59588 + 250516 + 374908 + 385752 + 129824 + 49872 + 285012 + 368632 + 340256
= 6814468
Value repetition frequencies = 4(47*3 + 1*3) +
4(38*1 + 1*3 + 1*9) +
4(36*1 + 1*2 + 1*3 + 1*9) +
4(38*1 + 2*2 + 1*8) +
4(41*1 + 1*2 + 1*7) +
4(39*1 + 1*2 + 1*9) +
4(2*1 + 1*48) +
4(34*1 + 1*2 + 1*14) +
4(32*1 + 1*5 + 1*13) +
4(37*1 + 1*13) +
2(3*2 + 1*44) +
2(3*2 + 1*4 + 1*40) +
2(7*1 + 19*2 + 1*5) +
2(7*1 + 19*2 + 1*5) +
2(7*1 + 19*2 + 1*5)
= 2500
Number of distinct row element sets = 15
Number of rows = 5*2 + 10*4
= 50
Number of distinct values = 421
Distinct values 0 1 2 3 6 19 20 29 72 114 198 214 221 249 252 271 281 291 295 306
Frequency 730 4 4 8 4 4 4 4 4 8 4 4 4 4 4 4 4 4 4 4
Distinct values 320 331 344 352 361 381 389 391 403 414 434 435 449 467 472 491 494 515 518 532
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 547 550 551 567 569 571 575 581 588 603 623 650 663 677 680 681 698 726 778 794
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 12 8
Distinct values 810 826 835 852 867 871 872 879 901 910 911 912 922 926 934 944 989 1000 1020 1056
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 24 4 4 4 4 4 4 4
Distinct values 1079 1082 1091 1092 1105 1114 1122 1134 1135 1154 1155 1158 1164 1168 1176 1240 1248 1299 1300 1320
Frequency 4 4 4 4 4 12 4 4 4 4 4 8 4 4 2 4 4 4 4 4
Distinct values 1326 1334 1343 1361 1398 1404 1431 1440 1452 1460 1480 1528 1534 1550 1556 1558 1606 1614 1628 1632
Frequency 4 4 4 4 4 4 4 4 2 4 4 8 4 4 8 4 4 4 8 2
Distinct values 1657 1658 1660 1663 1677 1686 1688 1695 1718 1720 1728 1734 1750 1760 1784 1814 1824 1828 1836 1837
Frequency 4 4 4 4 4 2 6 4 4 4 4 4 4 2 4 8 4 4 4 4
Distinct values 1840 1844 1850 1901 1935 1952 1958 1962 1980 2004 2010 2016 2017 2024 2028 2037 2038 2040 2064 2066
Frequency 4 8 4 4 4 4 4 4 4 8 8 2 4 4 4 4 4 4 4 4
Distinct values 2082 2092 2098 2139 2146 2165 2176 2178 2194 2208 2234 2244 2256 2264 2271 2285 2288 2296 2302 2338
Frequency 4 4 4 4 8 4 4 4 4 4 4 4 4 4 4 4 2 4 4 4
Distinct values 2344 2349 2383 2392 2402 2440 2446 2488 2493 2504 2512 2521 2532 2568 2569 2576 2580 2583 2610 2640
Frequency 4 4 4 6 4 4 2 4 4 4 4 4 2 4 4 4 8 4 4 4
Distinct values 2653 2654 2669 2694 2696 2709 2710 2719 2724 2738 2756 2766 2768 2769 2770 2852 2860 2928 2930 2934
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 2943 2958 2972 2983 3004 3037 3078 3102 3109 3116 3120 3151 3176 3188 3210 3262 3275 3280 3296 3328
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 12 4 4
Distinct values 3360 3366 3390 3404 3416 3436 3472 3508 3514 3516 3519 3520 3538 3545 3553 3592 3596 3634 3638 3694
Frequency 2 4 4 4 2 8 4 4 4 2 4 4 4 4 4 4 8 4 4 4
Distinct values 3704 3706 3721 3788 3792 3804 3838 3918 3927 3970 3980 4010 4036 4080 4092 4186 4201 4224 4228 4246
Frequency 4 4 4 4 4 4 4 4 4 4 8 4 4 4 4 4 4 4 2 4
Distinct values 4276 4287 4325 4339 4352 4384 4395 4428 4432 4444 4466 4488 4500 4530 4532 4537 4588 4608 4636 4650
Frequency 2 4 4 4 4 4 4 4 4 2 8 4 4 4 4 4 2 4 4 4
Distinct values 4672 4690 4710 4782 4787 4813 4840 4866 4888 4920 4950 4952 4956 4966 5003 5062 5072 5098 5105 5130
Frequency 4 4 4 4 4 4 4 4 2 4 4 4 4 4 4 4 4 2 4 4
Distinct values 5136 5142 5225 5243 5405 5434 5436 5540 5558 5641 5649 5659 5660 5662 5676 5692 5745 5780 5886 5931
Frequency 4 8 4 4 4 4 4 8 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 6046 6191 6224 6323 6468 6514 6526 6572 6581 6587 6744 6776 6804 6808 6840 6861 6894 6916 6925 7094
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 4 2 4 4 4 4 4
Distinct values 7113 7128 7200 7232 7288 7380 7407 7519 7558 7593 7643 7658 7741 7811 7879 7968 7981 7989 8113 8154
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 8249 8530 9029 9063 9467 9820 10202 10316 10506 10628 10630 11289 11367 11485 11487 11857 12021 12245 12768 12901
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 13415 13720 14095 14298 14329 14462 14901 14994 15045 15160 15301 15410 15847 15920 15990 16085 16287 16323 16444 19948
Frequency 4 4 4 4 4 4 4 4 4 8 4 4 4 4 4 4 4 4 4 4
Distinct values 20266
Frequency 4
Sum of distinct value frequencies = 19*2 + 375*4 + 2*6 + 20*8 + 3*12 + 1*24 + 1*730
= 2500
Number of SN-EN pairs for which the number of CNSAPs is greater than zero = 4*2 + 2*6 + 2*10 + 4*36 + 8*37 + 12*41 + 4*42 + 4*43 + 6*45 + 4*47
= 1770
Number of SN-EN pairs, with SN != EN, for which the number of CNSAPs equals zero = 680
Number of possible SN-EN pairs with SN != EN = 49*50
= 2450
a = 11, b = 5
L C
3 8
4 16
5 40
6 88
7 232
8 372
9 836
10 1352
11 3348
12 5112
13 13168
14 19980
15 48824
16 69124
17 146348
18 185924
19 345196
20 397476
21 690328
22 792532
23 1289576
24 1354676
25 2088732
26 1878068
27 2901520
28 2172964
29 3488824
30 2022484
31 2716996
32 1090480
33 565232
34 154428
35 33108
36 1892
37 12
Total 24479296
Number of times each node is the starting node (SN) in a CNSAP of each length (L)
SN 0 1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20 21
22 23 24 25 26 27 28 29 30 31 32
33 34 35 36 37 38 39 40 41 42 43
44 45 46 47 48 49 50 51 52 53 54
L
3 0 0 0 0 0 0 0 0 0 0 0
0 2 0 0 0 0 0 0 0 2 0
0 0 0 0 0 0 0 0 0 0 0
0 2 0 0 0 0 0 0 0 2 0
0 0 0 0 0 0 0 0 0 0 0
4 0 0 0 0 0 0 0 0 0 0 0
0 0 2 0 0 0 0 0 2 0 0
0 4 0 0 0 0 0 0 0 4 0
0 0 2 0 0 0 0 0 2 0 0
0 0 0 0 0 0 0 0 0 0 0
5 0 0 1 0 0 0 0 0 1 0 0
0 2 0 2 0 0 0 2 0 2 0
2 0 8 0 0 0 0 0 8 0 2
0 2 0 2 0 0 0 2 0 2 0
0 0 1 0 0 0 0 0 1 0 0
6 0 2 0 3 0 0 0 3 0 2 0
3 0 6 0 2 0 2 0 6 0 3
0 0 0 12 0 0 0 12 0 0 0
3 0 6 0 2 0 2 0 6 0 3
0 2 0 3 0 0 0 3 0 2 0
7 5 1 9 0 5 0 5 0 9 1 5
1 4 2 16 2 6 2 16 2 4 1
2 2 0 0 16 0 16 0 0 2 2
1 4 2 16 2 6 2 16 2 4 1
5 1 9 0 5 0 5 0 9 1 5
8 0 8 0 23 0 14 0 23 0 8 0
4 2 3 2 31 2 31 2 3 2 4
0 0 0 4 0 40 0 4 0 0 0
4 2 3 2 31 2 31 2 3 2 4
0 8 0 23 0 14 0 23 0 8 0
9 13 5 14 4 62 4 62 4 14 5 13
5 7 4 13 6 98 6 13 4 7 5
6 2 0 0 42 0 42 0 0 2 6
5 7 4 13 6 98 6 13 4 7 5
13 5 14 4 62 4 62 4 14 5 13
10 6 16 4 32 6 188 6 32 4 16 6
10 4 8 4 100 6 100 4 8 4 10
2 2 2 36 4 112 4 36 2 2 2
10 4 8 4 100 6 100 4 8 4 10
6 16 4 32 6 188 6 32 4 16 6
11 33 23 52 25 213 30 213 25 52 23 33
20 33 22 143 32 184 32 143 22 33 20
26 14 40 12 168 16 168 12 40 14 26
20 33 22 143 32 184 32 143 22 33 20
33 23 52 25 213 30 213 25 52 23 33
12 23 54 21 301 29 184 29 301 21 54 23
34 19 165 21 262 32 262 21 165 19 34
14 50 14 268 20 232 20 268 14 50 14
34 19 165 21 262 32 262 21 165 19 34
23 54 21 301 29 184 29 301 21 54 23
13 102 98 512 122 424 140 424 122 512 98 102
84 294 92 578 135 356 135 578 92 294 84
150 70 466 60 420 80 420 60 466 70 150
84 294 92 578 135 356 135 578 92 294 84
102 98 512 122 424 140 424 122 512 98 102
14 86 647 93 701 107 554 107 701 93 647 86
355 96 979 95 492 120 492 95 979 96 355
88 756 90 828 90 324 90 828 90 756 88
355 96 979 95 492 120 492 95 979 96 355
86 647 93 701 107 554 107 701 93 647 86
15 1016 353 1639 488 1345 546 1345 488 1639 353 1016
322 1950 360 1259 437 864 437 1259 360 1950 322
1400 338 1882 270 612 324 612 270 1882 338 1400
322 1950 360 1259 437 864 437 1259 360 1950 322
1016 353 1639 488 1345 546 1345 488 1639 353 1016
16 373 2737 391 2008 355 1538 355 2008 391 2737 373
3108 446 2445 393 986 308 986 393 2445 446 3108
438 3740 452 1072 286 488 286 1072 452 3740 438
3108 446 2445 393 986 308 986 393 2445 446 3108
373 2737 391 2008 355 1538 355 2008 391 2737 373
17 5233 1158 4756 1534 3528 1600 3528 1534 4756 1158 5233
1148 5776 1190 2437 1080 2008 1080 2437 1190 5776 1148
7558 1248 2780 858 1108 668 1108 858 2780 1248 7558
1148 5776 1190 2437 1080 2008 1080 2437 1190 5776 1148
5233 1158 4756 1534 3528 1600 3528 1534 4756 1158 5233
18 1530 8792 1492 4588 965 3606 965 4588 1492 8792 1530
11095 1717 4304 1266 2309 446 2309 1266 4304 1717 11095
1768 6358 1506 2094 624 888 624 2094 1506 6358 1768
11095 1717 4304 1266 2309 446 2309 1266 4304 1717 11095
1530 8792 1492 4588 965 3606 965 4588 1492 8792 1530
19 17299 3691 9777 3874 8265 3496 8265 3874 9777 3691 17299
3852 10361 3346 5457 2210 3962 2210 5457 3346 10361 3852
14964 3776 5366 2058 2412 600 2412 2058 5366 3776 14964
3852 10361 3346 5457 2210 3962 2210 5457 3346 10361 3852
17299 3691 9777 3874 8265 3496 8265 3874 9777 3691 17299
20 5525 16429 4508 10809 1931 8100 1931 10809 4508 16429 5525
19384 5335 9121 2729 5110 1120 5110 2729 9121 5335 19384
6016 11396 3830 4376 790 2696 790 4376 3830 11396 6016
19384 5335 9121 2729 5110 1120 5110 2729 9121 5335 19384
5525 16429 4508 10809 1931 8100 1931 10809 4508 16429 5525
21 25976 10451 21854 7607 17379 7544 17379 7607 21854 10451 25976
11507 18831 7470 11373 3698 9610 3698 11373 7470 18831 11507
26806 9754 9854 3492 5124 1376 5124 3492 9854 9754 26806
11507 18831 7470 11373 3698 9610 3698 11373 7470 18831 11507
25976 10451 21854 7607 17379 7544 17379 7607 21854 10451 25976
22 16407 30336 10095 22254 4153 17516 4153 22254 10095 30336 16407
32044 12883 15940 3540 12331 2878 12331 3540 15940 12883 32044
16964 18542 6620 7168 2256 8712 2256 7168 6620 18542 16964
32044 12883 15940 3540 12331 2878 12331 3540 15940 12883 32044
16407 30336 10095 22254 4153 17516 4153 22254 10095 30336 16407
23 46624 24000 37258 14445 34786 14780 34786 14445 37258 24000 46624
28489 31123 12352 20413 8078 22062 8078 20413 12352 31123 28489
40780 19082 12614 4550 13820 3928 13820 4550 12614 19082 40780
28489 31123 12352 20413 8078 22062 8078 20413 12352 31123 28489
46624 24000 37258 14445 34786 14780 34786 14445 37258 24000 46624
24 37643 48747 17966 35548 9011 34234 9011 35548 17966 48747 37643
49389 21102 19812 6688 24242 6612 24242 6688 19812 21102 49389
35360 21484 6462 15460 6026 22808 6026 15460 6462 21484 35360
49389 21102 19812 6688 24242 6612 24242 6688 19812 21102 49389
37643 48747 17966 35548 9011 34234 9011 35548 17966 48747 37643
25 71765 42557 58115 30328 55921 26278 55921 30328 58115 42557 71765
50838 38680 19366 31963 16889 40848 16889 31963 19366 38680 50838
60900 24506 16176 7806 29462 11092 29462 7806 16176 24506 60900
50838 38680 19366 31963 16889 40848 16889 31963 19366 38680 50838
71765 42557 58115 30328 55921 26278 55921 30328 58115 42557 71765
26 59182 58201 32532 54767 17738 41726 17738 54767 32532 58201 59182
61555 23047 25676 12694 32163 11472 32163 12694 25676 23047 61555
43882 18664 9246 24120 13982 41664 13982 24120 9246 18664 43882
61555 23047 25676 12694 32163 11472 32163 12694 25676 23047 61555
59182 58201 32532 54767 17738 41726 17738 54767 32532 58201 59182
27 86465 64311 84406 56873 75107 42874 75107 56873 84406 64311 86465
60079 50868 30660 48757 30646 44006 30646 48757 30660 50868 60079
70934 30446 18362 15332 40458 24008 40458 15332 18362 30446 70934
60079 50868 30660 48757 30646 44006 30646 48757 30660 50868 60079
86465 64311 84406 56873 75107 42874 75107 56873 84406 64311 86465
28 60179 70883 48876 64247 29918 43894 29918 64247 48876 70883 60179
57972 21936 29277 22983 34104 18024 34104 22983 29277 21936 57972
34400 13914 14050 37496 25360 37188 25360 37496 14050 13914 34400
57972 21936 29277 22983 34104 18024 34104 22983 29277 21936 57972
60179 70883 48876 64247 29918 43894 29918 64247 48876 70883 60179
29 93563 80204 105863 83269 82544 58296 82544 83269 105863 80204 93563
64573 52834 39711 57317 45185 50408 45185 57317 39711 52834 64573
80776 28160 20844 27968 48862 37944 48862 27968 20844 28160 80776
64573 52834 39711 57317 45185 50408 45185 57317 39711 52834 64573
93563 80204 105863 83269 82544 58296 82544 83269 105863 80204 93563
30 51592 59428 47288 55430 39101 48810 39101 55430 47288 59428 51592
45637 11350 26413 28086 30605 21904 30605 28086 26413 11350 45637
17706 8462 21818 46708 36214 39520 36214 46708 21818 8462 17706
45637 11350 26413 28086 30605 21904 30605 28086 26413 11350 45637
51592 59428 47288 55430 39101 48810 39101 55430 47288 59428 51592
31 71721 60550 78249 67304 64297 53308 64297 67304 78249 60550 71721
48303 28587 28561 41906 39612 41864 39612 41906 28561 28587 48303
65362 15694 22988 37590 45122 36780 45122 37590 22988 15694 65362
48303 28587 28561 41906 39612 41864 39612 41906 28561 28587 48303
71721 60550 78249 67304 64297 53308 64297 67304 78249 60550 71721
32 28740 27769 17453 20298 26955 38192 26955 20298 17453 27769 28740
18905 2864 13714 15537 17145 13762 17145 15537 13714 2864 18905
3760 7342 23730 39140 28324 24460 28324 39140 23730 7342 3760
18905 2864 13714 15537 17145 13762 17145 15537 13714 2864 18905
28740 27769 17453 20298 26955 38192 26955 20298 17453 27769 28740
33 20599 12626 12070 7425 15256 18730 15256 7425 12070 12626 20599
6583 2904 6512 6801 5716 8708 5716 6801 6512 2904 6583
8616 918 18528 18488 12066 7156 12066 18488 18528 918 8616
6583 2904 6512 6801 5716 8708 5716 6801 6512 2904 6583
20599 12626 12070 7425 15256 18730 15256 7425 12070 12626 20599
34 5473 5584 1744 2461 4039 7568 4039 2461 1744 5584 5473
1574 60 1245 581 967 540 967 581 1245 60 1574
36 756 8128 8852 2292 3172 2292 8852 8128 756 36
1574 60 1245 581 967 540 967 581 1245 60 1574
5473 5584 1744 2461 4039 7568 4039 2461 1744 5584 5473
35 1489 470 1092 203 1406 708 1406 203 1092 470 1489
177 36 260 212 313 404 313 212 260 36 177
322 4 2208 552 908 264 908 552 2208 4 322
177 36 260 212 313 404 313 212 260 36 177
1489 470 1092 203 1406 708 1406 203 1092 470 1489
36 63 77 29 62 57 42 57 62 29 77 63
0 0 23 4 24 24 24 4 23 0 0
0 26 116 0 30 60 30 0 116 26 0
0 0 23 4 24 24 24 4 23 0 0
63 77 29 62 57 42 57 62 29 77 63
37 0 2 0 0 0 0 0 0 0 2 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 4 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 2 0 0 0 0 0 0 0 2 0
Total 708725 630210 598159 547033 494903 474500 494903 547033 598159 630210 708725
577050 343153 299041 323270 314912 302638 314912 323270 299041 343153 577050
539038 245510 228180 306670 316898 306604 316898 306670 228180 245510 539038
577050 343153 299041 323270 314912 302638 314912 323270 299041 343153 577050
708725 630210 598159 547033 494903 474500 494903 547033 598159 630210 708725
Grand total = 2*228180 + 2*245510 + 4*299041 + 2*302638 + 1*306604 + 2*306670 + 4*314912 + 2*316898 + 4*323270 + 4*343153 + 2*474500 + 4*494903 + 2*539038 + 4*547033 + 4*577050 + 4*598159 + 4*630210 + 4*708725
= 24479296
Number of times each node is the ending node (EN) in a CNSAP of each length (L)
EN 0 1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20 21
22 23 24 25 26 27 28 29 30 31 32
33 34 35 36 37 38 39 40 41 42 43
44 45 46 47 48 49 50 51 52 53 54
L
3 2 0 0 0 0 0 0 0 0 0 2
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
2 0 0 0 0 0 0 0 0 0 2
4 4 0 0 0 0 0 0 0 0 0 4
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
4 0 0 0 0 0 0 0 0 0 4
5 10 0 0 0 0 0 0 0 0 0 10
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
10 0 0 0 0 0 0 0 0 0 10
6 22 0 0 0 0 0 0 0 0 0 22
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
22 0 0 0 0 0 0 0 0 0 22
7 46 2 2 2 2 2 2 2 2 2 46
2 0 0 0 0 0 0 0 0 0 2
2 0 0 0 0 0 0 0 0 0 2
2 0 0 0 0 0 0 0 0 0 2
46 2 2 2 2 2 2 2 2 2 46
8 83 1 2 2 2 2 2 2 2 1 83
1 0 0 0 0 0 0 0 0 0 1
2 0 0 0 0 0 0 0 0 0 2
1 0 0 0 0 0 0 0 0 0 1
83 1 2 2 2 2 2 2 2 1 83
9 159 6 9 10 10 10 10 10 9 6 159
6 0 0 0 0 0 0 0 0 0 6
8 0 0 0 0 0 0 0 0 0 8
6 0 0 0 0 0 0 0 0 0 6
159 6 9 10 10 10 10 10 9 6 159
10 282 6 9 13 14 14 14 13 9 6 282
5 0 0 0 0 0 0 0 0 0 5
4 0 0 0 0 0 0 0 0 0 4
5 0 0 0 0 0 0 0 0 0 5
282 6 9 13 14 14 14 13 9 6 282
11 536 26 44 49 55 56 55 49 44 26 536
19 4 8 8 8 8 8 8 8 4 19
32 8 16 16 16 16 16 16 16 8 32
19 4 8 8 8 8 8 8 8 4 19
536 26 44 49 55 56 55 49 44 26 536
12 989 26 43 58 65 72 65 58 43 26 989
11 0 4 4 4 4 4 4 4 0 11
12 4 16 16 16 16 16 16 16 4 12
11 0 4 4 4 4 4 4 4 0 11
989 26 43 58 65 72 65 58 43 26 989
13 1959 100 175 216 240 244 240 216 175 100 1959
60 20 44 56 56 56 56 56 44 20 60
88 32 72 96 96 96 96 96 72 32 88
60 20 44 56 56 56 56 56 44 20 60
1959 100 175 216 240 244 240 216 175 100 1959
14 3705 100 177 235 252 268 252 235 177 100 3705
20 0 32 46 48 48 48 46 32 0 20
24 16 88 124 128 128 128 124 88 16 24
20 0 32 46 48 48 48 46 32 0 20
3705 100 177 235 252 268 252 235 177 100 3705
15 7096 348 622 822 912 902 912 822 622 348 7096
175 72 174 278 306 308 306 278 174 72 175
232 84 240 380 436 440 436 380 240 84 232
175 72 174 278 306 308 306 278 174 72 175
7096 348 622 822 912 902 912 822 622 348 7096
16 12110 397 667 869 877 912 877 869 667 397 12110
63 0 141 258 306 320 306 258 141 0 63
44 30 318 564 656 684 656 564 318 30 44
63 0 141 258 306 320 306 258 141 0 63
12110 397 667 869 877 912 877 869 667 397 12110
17 20636 1118 1878 2352 2817 2826 2817 2352 1878 1118 20636
446 177 502 882 1148 1212 1148 882 502 177 446
548 196 726 1232 1648 1748 1648 1232 726 196 548
446 177 502 882 1148 1212 1148 882 502 177 446
20636 1118 1878 2352 2817 2826 2817 2352 1878 1118 20636
18 29114 1463 2139 2632 2703 2842 2703 2632 2139 1463 29114
221 0 446 965 1293 1330 1293 965 446 0 221
104 42 942 1950 2460 2680 2460 1950 942 42 104
221 0 446 965 1293 1330 1293 965 446 0 221
29114 1463 2139 2632 2703 2842 2703 2632 2139 1463 29114
19 43653 3179 5030 5889 7008 7460 7008 5889 5030 3179 43653
1059 357 1261 2456 3216 3738 3216 2456 1261 357 1059
1200 414 2054 3782 5022 5424 5022 3782 2054 414 1200
1059 357 1261 2456 3216 3738 3216 2456 1261 357 1059
43653 3179 5030 5889 7008 7460 7008 5889 5030 3179 43653
20 50576 4142 5835 6921 6936 7574 6936 6921 5835 4142 50576
698 0 1325 2813 4045 4240 4045 2813 1325 0 698
272 76 2800 5802 7294 8196 7294 5802 2800 76 272
698 0 1325 2813 4045 4240 4045 2813 1325 0 698
50576 4142 5835 6921 6936 7574 6936 6921 5835 4142 50576
21 71030 7355 12096 13732 15813 15560 15813 13732 12096 7355 71030
2525 674 3166 6153 8069 8932 8069 6153 3166 674 2525
2560 880 5706 10082 13490 13456 13490 10082 5706 880 2560
2525 674 3166 6153 8069 8932 8069 6153 3166 674 2525
71030 7355 12096 13732 15813 15560 15813 13732 12096 7355 71030
22 82784 8974 13285 16257 15531 16414 15531 16257 13285 8974 82784
1887 0 3565 6908 9888 10200 9888 6908 3565 0 1887
664 190 7496 14882 18016 20492 18016 14882 7496 190 664
1887 0 3565 6908 9888 10200 9888 6908 3565 0 1887
82784 8974 13285 16257 15531 16414 15531 16257 13285 8974 82784
23 108151 14469 25569 29249 31410 29412 31410 29249 25569 14469 108151
5549 1390 7321 14174 16454 19004 16454 14174 7321 1390 5549
5644 1940 14104 23066 29544 29204 29544 23066 14104 1940 5644
5549 1390 7321 14174 16454 19004 16454 14174 7321 1390 5549
108151 14469 25569 29249 31410 29412 31410 29249 25569 14469 108151
24 115467 15819 24449 31825 29023 30158 29023 31825 24449 15819 115467
3909 0 7685 14091 19022 18242 19022 14091 7685 0 3909
1536 486 17026 31940 35194 40352 35194 31940 17026 486 1536
3909 0 7685 14091 19022 18242 19022 14091 7685 0 3909
115467 15819 24449 31825 29023 30158 29023 31825 24449 15819 115467
25 137273 25691 46197 51103 53872 49422 53872 51103 46197 25691 137273
11834 3176 14513 26871 28241 30916 28241 26871 14513 3176 11834
12938 4458 29568 43126 52074 48644 52074 43126 29568 4458 12938
11834 3176 14513 26871 28241 30916 28241 26871 14513 3176 11834
137273 25691 46197 51103 53872 49422 53872 51103 46197 25691 137273
26 128618 23535 35947 47869 42848 45350 42848 47869 35947 23535 128618
7098 0 13093 23648 27812 22096 27812 23648 13093 0 7098
3466 1194 30352 55430 52030 56360 52030 55430 30352 1194 3466
7098 0 13093 23648 27812 22096 27812 23648 13093 0 7098
128618 23535 35947 47869 42848 45350 42848 47869 35947 23535 128618
27 141353 43075 70545 72627 76770 71300 76770 72627 70545 43075 141353
24438 7535 25011 42045 39465 39322 39465 42045 25011 7535 24438
29650 10378 48970 66356 70528 57056 70528 66356 48970 10378 29650
24438 7535 25011 42045 39465 39322 39465 42045 25011 7535 24438
141353 43075 70545 72627 76770 71300 76770 72627 70545 43075 141353
28 114576 29984 45168 55567 52918 58286 52918 55567 45168 29984 114576
11456 0 18834 30106 31553 26622 31553 30106 18834 0 11456
7494 2844 47440 76514 59772 54372 59772 76514 47440 2844 7494
11456 0 18834 30106 31553 26622 31553 30106 18834 0 11456
114576 29984 45168 55567 52918 58286 52918 55567 45168 29984 114576
29 132015 62303 87835 85029 88980 88002 88980 85029 87835 62303 132015
42443 14754 34427 49211 46543 46718 46543 49211 34427 14754 42443
53662 19394 64528 79174 74634 62440 74634 79174 64528 19394 53662
42443 14754 34427 49211 46543 46718 46543 49211 34427 14754 42443
132015 62303 87835 85029 88980 88002 88980 85029 87835 62303 132015
30 85235 30451 40528 47637 52751 62896 52751 47637 40528 30451 85235
15408 0 20930 28149 27924 25058 27924 28149 20930 0 15408
10162 5420 57934 75836 52286 47248 52286 75836 57934 5420 10162
15408 0 20930 28149 27924 25058 27924 28149 20930 0 15408
85235 30451 40528 47637 52751 62896 52751 47637 40528 30451 85235
31 89277 55859 66251 61568 68070 71172 68070 61568 66251 55859 89277
39286 14812 27609 36494 35466 35738 35466 36494 27609 14812 39286
47834 16812 57164 62140 54312 47884 54312 62140 57164 16812 47834
39286 14812 27609 36494 35466 35738 35466 36494 27609 14812 39286
89277 55859 66251 61568 68070 71172 68070 61568 66251 55859 89277
32 41064 20182 17676 20914 30911 39804 30911 20914 17676 20182 41064
9471 0 11725 13406 13867 12236 13867 13406 11725 0 9471
3668 5054 43568 43028 26980 24940 26980 43028 43568 5054 3668
9471 0 11725 13406 13867 12236 13867 13406 11725 0 9471
41064 20182 17676 20914 30911 39804 30911 20914 17676 20182 41064
33 22598 12331 11077 8758 16427 19162 16427 8758 11077 12331 22598
5047 1074 5720 5072 5179 5864 5179 5072 5720 1074 5047
6964 1620 26148 19472 11706 10228 11706 19472 26148 1620 6964
5047 1074 5720 5072 5179 5864 5179 5072 5720 1074 5047
22598 12331 11077 8758 16427 19162 16427 8758 11077 12331 22598
34 6536 4270 2335 2368 4856 6034 4856 2368 2335 4270 6536
980 0 1105 653 971 676 971 653 1105 0 980
164 746 10124 6872 2700 3500 2700 6872 10124 746 164
980 0 1105 653 971 676 971 653 1105 0 980
6536 4270 2335 2368 4856 6034 4856 2368 2335 4270 6536
35 1473 475 1042 262 1418 616 1418 262 1042 475 1473
159 36 246 214 322 420 322 214 246 36 159
296 30 2324 504 906 328 906 504 2324 30 296
159 36 246 214 322 420 322 214 246 36 159
1473 475 1042 262 1418 616 1418 262 1042 475 1473
36 61 79 29 62 57 42 57 62 29 79 61
0 0 23 4 24 24 24 4 23 0 0
0 26 116 0 28 64 28 0 116 26 0
0 0 23 4 24 24 24 4 23 0 0
61 79 29 62 57 42 57 62 29 79 61
37 0 2 0 0 0 0 0 0 0 2 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 4 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 2 0 0 0 0 0 0 0 2 0
Total 1448493 365768 516661 564897 603548 626814 603548 564897 516661 365768 1448493
184276 44081 198910 304965 321230 313332 321230 304965 198910 44081 184276
189274 72374 469840 622384 571972 536000 571972 622384 469840 72374 189274
184276 44081 198910 304965 321230 313332 321230 304965 198910 44081 184276
1448493 365768 516661 564897 603548 626814 603548 564897 516661 365768 1448493
Grand total = 4*44081 + 2*72374 + 4*184276 + 2*189274 + 4*198910 + 4*304965 + 2*313332 + 4*321230 + 4*365768 + 2*469840 + 4*516661 + 1*536000 + 4*564897 + 2*571972 + 4*603548 + 2*622384 + 2*626814 + 4*1448493
= 24479296
Number of times each node (N) is present in a CNSAP of each length (L)
N 0 1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20 21
22 23 24 25 26 27 28 29 30 31 32
33 34 35 36 37 38 39 40 41 42 43
44 45 46 47 48 49 50 51 52 53 54
L
3 2 1 0 0 0 0 0 0 0 1 2
1 2 0 0 0 0 0 0 0 2 1
0 0 0 0 0 0 0 0 0 0 0
1 2 0 0 0 0 0 0 0 2 1
2 1 0 0 0 0 0 0 0 1 2
4 4 2 0 0 0 0 0 0 0 2 4
2 4 2 0 0 0 0 0 2 4 2
0 4 0 0 0 0 0 0 0 4 0
2 4 2 0 0 0 0 0 2 4 2
4 2 0 0 0 0 0 0 0 2 4
5 10 5 1 0 0 0 0 0 1 5 10
5 12 5 2 0 0 0 2 5 12 5
2 10 8 0 0 0 0 0 8 10 2
5 12 5 2 0 0 0 2 5 12 5
10 5 1 0 0 0 0 0 1 5 10
6 22 13 1 3 0 0 0 3 1 13 22
14 28 17 6 2 0 2 6 17 28 14
2 22 16 12 0 0 0 12 16 22 2
14 28 17 6 2 0 2 6 17 28 14
22 13 1 3 0 0 0 3 1 13 22
7 53 32 17 7 9 4 9 7 17 32 53
31 60 47 30 10 8 10 30 47 60 31
14 58 62 40 28 12 28 40 62 58 14
31 60 47 30 10 8 10 30 47 60 31
53 32 17 7 9 4 9 7 17 32 53
8 86 54 20 31 10 18 10 31 20 54 86
50 101 87 62 47 18 47 62 87 101 50
10 78 106 84 52 52 52 84 106 78 10
50 101 87 62 47 18 47 62 87 101 50
86 54 20 31 10 18 10 31 20 54 86
9 183 113 61 69 94 46 94 69 61 113 183
113 206 183 157 124 148 124 157 183 206 113
44 166 240 226 202 168 202 226 240 166 44
113 206 183 157 124 148 124 157 183 206 113
183 113 61 69 94 46 94 69 61 113 183
10 308 191 77 120 144 258 144 120 77 191 308
178 346 293 265 334 318 334 265 293 346 178
34 266 348 400 400 448 400 400 348 266 34
178 346 293 265 334 318 334 265 293 346 178
308 191 77 120 144 258 144 120 77 191 308
11 630 439 312 370 565 552 565 370 312 439 630
438 807 765 912 909 1046 909 912 765 807 438
220 630 824 1052 1194 1204 1194 1052 824 630 220
438 807 765 912 909 1046 909 912 765 807 438
630 439 312 370 565 552 565 370 312 439 630
12 1083 706 384 804 870 992 870 804 384 706 1083
660 1316 1282 1386 1746 1754 1746 1386 1282 1316 660
164 1046 1326 1770 2014 2264 2014 1770 1326 1046 164
660 1316 1282 1386 1746 1754 1746 1386 1282 1316 660
1083 706 384 804 870 992 870 804 384 706 1083
13 2379 1880 1955 2381 2859 2796 2859 2381 1955 1880 2379
1741 3350 3385 4300 4689 4880 4689 4300 3385 3350 1741
990 2688 3700 4484 5460 5512 5460 4484 3700 2688 990
1741 3350 3385 4300 4689 4880 4689 4300 3385 3350 1741
2379 1880 1955 2381 2859 2796 2859 2381 1955 1880 2379
14 4112 3300 2421 3864 4309 4768 4309 3864 2421 3300 4112
2826 5636 6200 6600 7623 7834 7623 6600 6200 5636 2826
930 5076 6432 7976 8578 8968 8578 7976 6432 5076 930
2826 5636 6200 6600 7623 7834 7623 6600 6200 5636 2826
4112 3300 2421 3864 4309 4768 4309 3864 2421 3300 4112
15 9428 8062 8983 11301 13707 13768 13707 11301 8983 8062 9428
6945 14447 14852 17223 19242 20190 19242 17223 14852 14447 6945
4912 12454 16738 18588 20644 21012 20644 18588 16738 12454 4912
6945 14447 14852 17223 19242 20190 19242 17223 14852 14447 6945
9428 8062 8983 11301 13707 13768 13707 11301 8983 8062 9428
16 14318 13316 11185 16469 18942 20824 18942 16469 11185 13316 14318
12174 22794 24655 25664 27700 28222 27700 25664 24655 22794 12174
5574 23064 28050 29674 28844 28612 28844 29674 28050 23064 5574
12174 22794 24655 25664 27700 28222 27700 25664 24655 22794 12174
14318 13316 11185 16469 18942 20824 18942 16469 11185 13316 14318
17 30886 27781 31811 40972 49967 52824 49967 40972 31811 27781 30886
24915 50442 51635 56236 59435 64614 59435 56236 51635 50442 24915
21750 48896 58500 59276 58758 62360 58758 59276 58500 48896 21750
24915 50442 51635 56236 59435 64614 59435 56236 51635 50442 24915
30886 27781 31811 40972 49967 52824 49967 40972 31811 27781 30886
18 38964 42741 40881 55418 63084 67894 63084 55418 40881 42741 38964
40156 69865 73186 74546 76828 76138 76828 74546 73186 69865 40156
27230 74144 83178 81190 75432 73544 75432 81190 83178 74144 27230
40156 69865 73186 74546 76828 76138 76828 74546 73186 69865 40156
38964 42741 40881 55418 63084 67894 63084 55418 40881 42741 38964
19 78874 79946 93024 116736 139179 141944 139179 116736 93024 79946 78874
73562 133810 135939 144339 149220 146006 149220 144339 135939 133810 73562
68958 135578 148468 144144 140520 128972 140520 144144 148468 135578 68958
73562 133810 135939 144339 149220 146006 149220 144339 135939 133810 73562
78874 79946 93024 116736 139179 141944 139179 116736 93024 79946 78874
20 87686 109310 117809 147122 154762 160834 154762 147122 117809 109310 87686
102513 163933 170644 171779 173160 169030 173160 171779 170644 163933 102513
89234 171532 176004 170330 161174 158372 161174 170330 176004 171532 89234
102513 163933 170644 171779 173160 169030 173160 171779 170644 163933 102513
87686 109310 117809 147122 154762 160834 154762 147122 117809 109310 87686
21 155878 194842 242429 284156 310052 308520 310052 284156 242429 194842 155878
181325 294202 300898 315827 302602 302266 302602 315827 300898 294202 181325
188108 299490 302056 292314 264654 253228 264654 292314 302056 299490 188108
181325 294202 300898 315827 302602 302266 302602 315827 300898 294202 181325
155878 194842 242429 284156 310052 308520 310052 284156 242429 194842 155878
22 189126 264939 303402 349112 345673 351396 345673 349112 303402 264939 189126
246933 363065 363716 350778 349621 343768 349621 350778 363716 363065 246933
246864 373412 353416 327278 310790 316396 310790 327278 353416 373412 246864
246933 363065 363716 350778 349621 343768 349621 350778 363716 363065 246933
189126 264939 303402 349112 345673 351396 345673 349112 303402 264939 189126
23 314722 446804 564081 617609 637036 623610 637036 617609 564081 446804 314722
418435 604885 610253 594652 574649 582518 574649 594652 610253 604885 418435
458206 620272 578634 496294 472242 464192 472242 496294 578634 620272 458206
418435 604885 610253 594652 574649 582518 574649 594652 610253 604885 418435
314722 446804 564081 617609 637036 623610 637036 617609 564081 446804 314722
24 366870 541610 626950 681796 654114 654758 654114 681796 626950 541610 366870
518956 678985 640937 604624 611493 605050 611493 604624 640937 678985 518956
561374 691274 579188 518214 519358 548452 519358 518214 579188 691274 561374
518956 678985 640937 604624 611493 605050 611493 604624 640937 678985 518956
366870 541610 626950 681796 654114 654758 654114 681796 626950 541610 366870
25 562436 865146 1083025 1137576 1127723 1086292 1127723 1137576 1083025 865146 562436
834063 1079582 1023060 966804 963806 982836 963806 966804 1023060 1079582 834063
960218 1105210 878236 704698 732236 745964 732236 704698 878236 1105210 960218
834063 1079582 1023060 966804 963806 982836 963806 966804 1023060 1079582 834063
562436 865146 1083025 1137576 1127723 1086292 1127723 1137576 1083025 865146 562436
26 577317 872329 1023042 1069926 996718 972312 996718 1069926 1023042 872329 577317
878971 1009134 903222 847353 873435 868558 873435 847353 903222 1009134 878971
994634 1004464 729606 649128 707516 771544 707516 649128 729606 1004464 994634
878971 1009134 903222 847353 873435 868558 873435 847353 903222 1009134 878971
577317 872329 1023042 1069926 996718 972312 996718 1069926 1023042 872329 577317
27 878884 1432613 1763404 1785622 1667526 1571184 1667526 1785622 1763404 1432613 878884
1425535 1629919 1406392 1367613 1391455 1416970 1391455 1367613 1406392 1629919 1425535
1701498 1616502 1006096 851254 985590 1047000 985590 851254 1006096 1616502 1701498
1425535 1629919 1406392 1367613 1391455 1416970 1391455 1367613 1406392 1629919 1425535
878884 1432613 1763404 1785622 1667526 1571184 1667526 1785622 1763404 1432613 878884
28 769405 1198983 1385457 1368838 1220508 1159946 1220508 1368838 1385457 1198983 769405
1233658 1215473 1023225 1011140 1043156 1035658 1043156 1011140 1023225 1215473 1233658
1433186 1142998 703308 726846 834630 890476 834630 726846 703308 1142998 1433186
1233658 1215473 1023225 1011140 1043156 1035658 1043156 1011140 1023225 1215473 1233658
769405 1198983 1385457 1368838 1220508 1159946 1220508 1368838 1385457 1198983 769405
29 1301967 2051514 2459610 2355359 2058551 1907044 2058551 2355359 2459610 2051514 1301967
2189971 1926221 1627770 1669938 1737798 1756390 1737798 1669938 1627770 1926221 2189971
2656640 1737936 941616 961040 1219680 1300408 1219680 961040 941616 1737936 2656640
2189971 1926221 1627770 1669938 1737798 1756390 1737798 1669938 1627770 1926221 2189971
1301967 2051514 2459610 2355359 2058551 1907044 2058551 2355359 2459610 2051514 1301967
30 877230 1303427 1489935 1382529 1187677 1114290 1187677 1382529 1489935 1303427 877230
1403162 1060918 923036 957228 989935 980476 989935 957228 923036 1060918 1403162
1652412 925962 562820 691332 826946 865736 826946 691332 562820 925962 1652412
1403162 1060918 923036 957228 989935 980476 989935 957228 923036 1060918 1403162
877230 1303427 1489935 1382529 1187677 1114290 1187677 1382529 1489935 1303427 877230
31 1296823 1897807 2225615 1973352 1639163 1500950 1639163 1973352 2225615 1897807 1296823
2069215 1310723 1191716 1293422 1369454 1380466 1369454 1293422 1191716 1310723 2069215
2513220 1072750 593230 820340 1103918 1187968 1103918 820340 593230 1072750 2513220
2069215 1310723 1191716 1293422 1369454 1380466 1369454 1293422 1191716 1310723 2069215
1296823 1897807 2225615 1973352 1639163 1500950 1639163 1973352 2225615 1897807 1296823
32 576161 813364 911881 789359 678757 646250 678757 789359 911881 813364 576161
867008 499323 473638 520397 547688 544802 547688 520397 473638 499323 867008
1023768 417638 290858 426956 491374 501764 491374 426956 290858 417638 1023768
867008 499323 473638 520397 547688 544802 547688 520397 473638 499323 867008
576161 813364 911881 789359 678757 646250 678757 789359 911881 813364 576161
33 327681 449616 492771 380842 375982 392140 375982 380842 492771 449616 327681
462161 237723 261375 268098 281853 285796 281853 268098 261375 237723 462161
545880 185072 179572 265070 269276 254636 269276 265070 179572 185072 545880
462161 237723 261375 268098 281853 285796 281853 268098 261375 237723 462161
327681 449616 492771 380842 375982 392140 375982 380842 492771 449616 327681
34 98786 133255 137737 104261 106552 118038 106552 104261 137737 133255 98786
131134 57445 66897 71469 73385 78022 73385 71469 66897 57445 131134
150292 46928 63382 92574 76964 74468 76964 92574 63382 46928 150292
131134 57445 66897 71469 73385 78022 73385 71469 66897 57445 131134
98786 133255 137737 104261 106552 118038 106552 104261 137737 133255 98786
35 23600 30717 31209 18349 25087 29558 25087 18349 31209 30717 23600
29280 10273 15226 12930 15708 14904 15708 12930 15226 10273 29280
32874 7038 19196 23988 20558 13032 20558 23988 19196 7038 32874
29280 10273 15226 12930 15708 14904 15708 12930 15226 10273 29280
23600 30717 31209 18349 25087 29558 25087 18349 31209 30717 23600
36 1516 1834 1718 914 1450 1892 1450 914 1718 1834 1516
1762 392 1118 664 1070 800 1070 664 1118 392 1762
1892 260 1420 1236 1436 488 1436 1236 1420 260 1892
1762 392 1118 664 1070 800 1070 664 1118 392 1762
1516 1834 1718 914 1450 1892 1450 914 1718 1834 1516
37 12 12 8 4 12 12 12 4 8 12 12
12 0 12 8 8 0 8 8 12 0 12
12 0 8 0 8 12 8 0 8 0 12
12 0 12 8 8 0 8 8 12 0 12
12 12 8 4 12 12 12 4 8 12 12
Total 8587442 12786704 15051216 14695271 13481082 12905714 13481082 14695271 15051216 12786704 8587442
13157905 12445422 11315668 11356452 11648185 11699486 11648185 11356452 11315668 12445422 13157905
15341146 11722918 8306642 8367808 9340476 9727264 9340476 8367808 8306642 11722918 15341146
13157905 12445422 11315668 11356452 11648185 11699486 11648185 11356452 11315668 12445422 13157905
8587442 12786704 15051216 14695271 13481082 12905714 13481082 14695271 15051216 12786704 8587442
Grand total = 2*8306642 + 2*8367808 + 4*8587442 + 2*9340476 + 1*9727264 + 4*11315668 + 4*11356452 + 4*11648185 + 2*11699486 + 2*11722918 + 4*12445422 + 4*12786704 + 2*12905714 + 4*13157905 + 4*13481082 + 4*14695271 + 4*15051216 +
2*15341146
= 663197032
Number of CNSAPs for each starting node (SN) and ending node (EN) pair
SN 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54
EN
0 0 0 59471 46950 40806 30935 28890 32807 38961 41863 46133 0 2 13666 28487 29007 22273 18528 18622 19557 21954 35671 58119 8015 6288 16488 20118 20985 22586 22373 17373 15995 32534 47495 21977 12329 8951
10306 17903 24698 25841 22657 22555 36603 46848 32757 22228 17732 20216 29142 36527 41155 43501 43512 48103
1 0 0 0 45523 1725 2413 2699 8708 11731 11565 12116 44310 0 21426 13790 3 29 1608 4815 6105 5899 8817 0 0 7738 4600 4739 7143 5226 4437 3711 3584 7270 0 0 0 2623
7632 7974 5830 3856 3218 4088 7310 3294 3294 3294 6145 9768 8673 7426 6407 6669 7588 8949
2 44597 0 0 0 47454 1494 5034 6354 14120 16100 16848 15160 35548 0 32807 13122 20 114 3588 7146 8328 12446 0 0 4456 12445 3820 7800 11140 7706 5256 5104 10516 1114 0 0 0
5532 15782 12940 8048 5344 5980 10890 2228 2228 2228 4456 12202 17798 14108 11726 10756 11270 13508
3 24381 48512 0 0 0 41090 1477 7165 8709 13769 15269 5883 5105 25661 0 33509 11035 448 651 4516 7474 12084 5883 0 5086 8433 12138 3130 9808 11132 6433 5341 11280 6272 2680 0 0
0 9717 20928 14274 8485 7491 13108 6272 7450 4599 3149 7428 18456 22909 18202 15851 14945 17279
4 12477 10615 49301 0 0 0 40438 2380 7109 8009 10669 9243 2572 10810 24108 0 29486 12075 1005 1571 5004 9863 9591 3866 2744 9813 9941 11142 3721 9108 7617 5296 10733 11169 9020 5686 0
0 0 11497 19758 12669 9155 14187 14467 17090 15992 8665 5454 10566 21936 25687 21294 18737 20212
5 8339 7536 4863 44880 0 0 0 44880 4863 7536 8339 8867 3550 1538 13634 26073 0 26073 13634 1538 3550 8867 10467 5708 6189 4551 11169 10290 11169 4551 6189 5708 10467 13815 10828 14498 9421
0 0 0 9421 14498 10828 13815 20247 20393 25308 21688 11319 6762 11319 21688 25308 20393 20247
6 10669 8009 7109 2380 40438 0 0 0 49301 10615 12477 9863 5004 1571 1005 12075 29486 0 24108 10810 2572 9243 10733 5296 7617 9108 3721 11142 9941 9813 2744 3866 9591 14187 9155 12669 19758
11497 0 0 0 5686 9020 11169 20212 18737 21294 25687 21936 10566 5454 8665 15992 17090 14467
7 15269 13769 8709 7165 1477 41090 0 0 0 48512 24381 12084 7474 4516 651 448 11035 33509 0 25661 5105 5883 11280 5341 6433 11132 9808 3130 12138 8433 5086 0 5883 13108 7491 8485 14274
20928 9717 0 0 0 2680 6272 17279 14945 15851 18202 22909 18456 7428 3149 4599 7450 6272
8 16848 16100 14120 6354 5034 1494 47454 0 0 0 44597 12446 8328 7146 3588 114 20 13122 32807 0 35548 15160 10516 5104 5256 7706 11140 7800 3820 12445 4456 0 0 10890 5980 5344 8048
12940 15782 5532 0 0 0 1114 13508 11270 10756 11726 14108 17798 12202 4456 2228 2228 2228
9 12116 11565 11731 8708 2699 2413 1725 45523 0 0 0 8817 5899 6105 4815 1608 29 3 13790 21426 0 44310 7270 3584 3711 4437 5226 7143 4739 4600 7738 0 0 7310 4088 3218 3856
5830 7974 7632 2623 0 0 0 8949 7588 6669 6407 7426 8673 9768 6145 3294 3294 3294
10 46133 41863 38961 32807 28890 30935 40806 46950 59471 0 0 35671 21954 19557 18622 18528 22273 29007 28487 13666 2 0 32534 15995 17373 22373 22586 20985 20118 16488 6288 8015 58119 36603 22555 22657 25841
24698 17903 10306 8951 12329 21977 47495 48103 43512 43501 41155 36527 29142 20216 17732 22228 32757 46848
11 0 44310 0 0 1765 1774 1450 1379 1638 1906 2161 0 0 0 0 1594 1440 1009 755 786 1019 1733 0 19948 2754 910 1089 785 984 1104 895 827 1675 41835 2293 0 1
3 6 1038 1587 1429 1281 1988 19195 2293 1718 604 215 681 1917 2603 2692 2509 2698
12 0 0 20388 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 23693 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
13 15340 15985 0 17026 4928 2086 1860 2486 3979 4659 4967 15340 0 0 0 7761 19 1195 1087 1959 2441 3767 7981 13139 0 3971 2541 531 2821 2617 1798 1616 3318 0 0 0 0
0 3222 5337 3530 2127 2064 3618 0 0 0 0 2376 6044 5915 4748 4081 3990 4640
14 14745 13898 22634 0 16063 9284 4588 4416 5206 6806 7730 7796 11244 0 0 0 14100 114 2650 2322 3718 6366 2654 2654 6114 0 7450 4088 986 4854 3792 3128 6328 2654 0 0 0
0 0 7720 10324 6374 4796 7740 2654 1605 0 0 0 6248 14384 13364 11106 9620 10648
15 9394 6684 10294 23635 0 18208 9742 4964 5195 5379 6555 6052 2710 12647 0 0 0 17150 381 2713 3089 6073 4498 922 3450 5038 0 8034 5309 1409 3892 3654 7002 5420 2766 0 0
0 0 0 8174 9801 6772 9262 6342 6732 3414 0 0 0 8019 17382 16257 13314 13502
16 6160 5492 4472 8544 21158 0 21158 8544 4472 5492 6160 5456 2968 1020 15752 0 0 0 15752 1020 2968 5456 6216 3024 1248 5280 6712 0 6712 5280 1248 3024 6216 7904 6752 5280 0
0 0 0 0 5280 6752 7904 11280 12168 13400 6380 0 0 0 6380 13400 12168 11280
17 6555 5379 5195 4964 9742 18208 0 23635 10294 6684 9394 6073 3089 2713 381 17150 0 0 0 12647 2710 6052 7002 3654 3892 1409 5309 8034 0 5038 3450 922 4498 9262 6772 9801 8174
0 0 0 0 0 2766 5420 13502 13314 16257 17382 8019 0 0 0 3414 6732 6342
18 7730 6806 5206 4416 4588 9284 16063 0 22634 13898 14745 6366 3718 2322 2650 114 14100 0 0 0 11244 7796 6328 3128 3792 4854 986 4088 7450 0 6114 2654 2654 7740 4796 6374 10324
7720 0 0 0 0 0 2654 10648 9620 11106 13364 14384 6248 0 0 0 1605 2654
19 4967 4659 3979 2486 1860 2086 4928 17026 0 15985 15340 3767 2441 1959 1087 1195 19 7761 0 0 0 15340 3318 1616 1798 2617 2821 531 2541 3971 0 13139 7981 3618 2064 2127 3530
5337 3222 0 0 0 0 0 4640 3990 4081 4748 5915 6044 2376 0 0 0 0
20 0 0 0 0 0 0 0 0 20388 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 23693 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
21 2161 1906 1638 1379 1450 1774 1765 0 0 44310 0 1733 1019 786 755 1009 1440 1594 0 0 0 0 1675 827 895 1104 984 785 1089 910 2754 19948 0 1988 1281 1429 1587
1038 6 3 1 0 2293 41835 2698 2509 2692 2603 1917 681 215 604 1718 2293 19195
22 43328 13808 0 0 0 0 0 0 0 0 0 0 37501 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 37501 0 0
0 0 0 0 0 0 0 43328 13808 0 0 0 0 0 0 0 0 0
23 5259 5259 2805 0 0 0 0 0 0 0 0 14901 0 7963 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 14901 0 7963 0
0 0 0 0 0 0 0 5259 5259 2805 0 0 0 0 0 0 0 0
24 13832 16706 10556 6100 4276 7516 10972 12272 13352 13752 15160 17060 9656 0 5442 2692 3576 6952 7324 6828 7164 11616 20288 0 0 0 6352 3152 6352 6928 5552 5152 10456 17060 9656 0 5442
2692 3576 6952 7324 6828 7164 11616 13832 16706 10556 6100 4276 7516 10972 12272 13352 13752 15160
25 18465 13815 16613 10901 9314 7083 12273 19172 20470 20493 22578 13335 9165 10433 0 6483 5183 5128 11152 10509 10678 17283 12720 10260 0 0 0 12584 4650 9612 8240 7700 15566 13335 9165 10433 0
6483 5183 5128 11152 10509 10678 17283 18465 13815 16613 10901 9314 7083 12273 19172 20470 20493 22578
26 18466 13398 8964 11560 9122 10100 6910 12984 20628 20276 21810 13984 5812 5464 11416 0 9554 5576 4524 10410 10586 16652 12036 4656 9376 0 0 0 14948 4572 7412 7524 15056 13984 5812 5464 11416
0 9554 5576 4524 10410 10586 16652 18466 13398 8964 11560 9122 10100 6910 12984 20628 20276 21810
27 19580 18120 12312 6734 9840 8556 9840 6734 12312 18120 19580 14908 9468 4094 4892 11310 0 11310 4892 4094 9468 14908 13400 6576 3932 13020 0 0 0 13020 3932 6576 13400 14908 9468 4094 4892
11310 0 11310 4892 4094 9468 14908 19580 18120 12312 6734 9840 8556 9840 6734 12312 18120 19580
28 21810 20276 20628 12984 6910 10100 9122 11560 8964 13398 18466 16652 10586 10410 4524 5576 9554 0 11416 5464 5812 13984 15056 7524 7412 4572 14948 0 0 0 9376 4656 12036 16652 10586 10410 4524
5576 9554 0 11416 5464 5812 13984 21810 20276 20628 12984 6910 10100 9122 11560 8964 13398 18466
29 22578 20493 20470 19172 12273 7083 9314 10901 16613 13815 18465 17283 10678 10509 11152 5128 5183 6483 0 10433 9165 13335 15566 7700 8240 9612 4650 12584 0 0 0 10260 12720 17283 10678 10509 11152
5128 5183 6483 0 10433 9165 13335 22578 20493 20470 19172 12273 7083 9314 10901 16613 13815 18465
30 15160 13752 13352 12272 10972 7516 4276 6100 10556 16706 13832 11616 7164 6828 7324 6952 3576 2692 5442 0 9656 17060 10456 5152 5552 6928 6352 3152 6352 0 0 0 20288 11616 7164 6828 7324
6952 3576 2692 5442 0 9656 17060 15160 13752 13352 12272 10972 7516 4276 6100 10556 16706 13832
31 0 0 0 0 0 0 0 0 2805 5259 5259 0 0 0 0 0 0 0 0 7963 0 14901 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 7963 0 14901 0 0 0 0 0 0 0 0 2805 5259 5259
32 0 0 0 0 0 0 0 0 0 13808 43328 0 0 0 0 0 0 0 0 0 37501 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 37501 0 0 0 0 0 0 0 0 0 0 13808 43328
33 19195 2293 1718 604 215 681 1917 2603 2692 2509 2698 41835 2293 0 1 3 6 1038 1587 1429 1281 1988 0 19948 2754 910 1089 785 984 1104 895 827 1675 0 0 0 0
1594 1440 1009 755 786 1019 1733 0 44310 0 0 1765 1774 1450 1379 1638 1906 2161
34 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 23693 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 20388 0 0 0 0 0 0 0 0
35 0 0 0 0 2376 6044 5915 4748 4081 3990 4640 0 0 0 0 0 3222 5337 3530 2127 2064 3618 7981 13139 0 3971 2541 531 2821 2617 1798 1616 3318 15340 0 0 0
7761 19 1195 1087 1959 2441 3767 15340 15985 0 17026 4928 2086 1860 2486 3979 4659 4967
36 2654 1605 0 0 0 6248 14384 13364 11106 9620 10648 2654 0 0 0 0 0 7720 10324 6374 4796 7740 2654 2654 6114 0 7450 4088 986 4854 3792 3128 6328 7796 11244 0 0
0 14100 114 2650 2322 3718 6366 14745 13898 22634 0 16063 9284 4588 4416 5206 6806 7730
37 6342 6732 3414 0 0 0 8019 17382 16257 13314 13502 5420 2766 0 0 0 0 0 8174 9801 6772 9262 4498 922 3450 5038 0 8034 5309 1409 3892 3654 7002 6052 2710 12647 0
0 0 17150 381 2713 3089 6073 9394 6684 10294 23635 0 18208 9742 4964 5195 5379 6555
38 11280 12168 13400 6380 0 0 0 6380 13400 12168 11280 7904 6752 5280 0 0 0 0 0 5280 6752 7904 6216 3024 1248 5280 6712 0 6712 5280 1248 3024 6216 5456 2968 1020 15752
0 0 0 15752 1020 2968 5456 6160 5492 4472 8544 21158 0 21158 8544 4472 5492 6160
39 13502 13314 16257 17382 8019 0 0 0 3414 6732 6342 9262 6772 9801 8174 0 0 0 0 0 2766 5420 7002 3654 3892 1409 5309 8034 0 5038 3450 922 4498 6073 3089 2713 381
17150 0 0 0 12647 2710 6052 6555 5379 5195 4964 9742 18208 0 23635 10294 6684 9394
40 10648 9620 11106 13364 14384 6248 0 0 0 1605 2654 7740 4796 6374 10324 7720 0 0 0 0 0 2654 6328 3128 3792 4854 986 4088 7450 0 6114 2654 2654 6366 3718 2322 2650
114 14100 0 0 0 11244 7796 7730 6806 5206 4416 4588 9284 16063 0 22634 13898 14745
41 4640 3990 4081 4748 5915 6044 2376 0 0 0 0 3618 2064 2127 3530 5337 3222 0 0 0 0 0 3318 1616 1798 2617 2821 531 2541 3971 0 13139 7981 3767 2441 1959 1087
1195 19 7761 0 0 0 15340 4967 4659 3979 2486 1860 2086 4928 17026 0 15985 15340
42 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 23693 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 20388 0 0
43 2698 2509 2692 2603 1917 681 215 604 1718 2293 19195 1988 1281 1429 1587 1038 6 3 1 0 2293 41835 1675 827 895 1104 984 785 1089 910 2754 19948 0 1733 1019 786 755
1009 1440 1594 0 0 0 0 2161 1906 1638 1379 1450 1774 1765 0 0 44310 0
44 46848 32757 22228 17732 20216 29142 36527 41155 43501 43512 48103 47495 21977 12329 8951 10306 17903 24698 25841 22657 22555 36603 58119 8015 6288 16488 20118 20985 22586 22373 17373 15995 32534 0 2 13666 28487
29007 22273 18528 18622 19557 21954 35671 0 0 59471 46950 40806 30935 28890 32807 38961 41863 46133
45 3294 3294 3294 6145 9768 8673 7426 6407 6669 7588 8949 0 0 0 2623 7632 7974 5830 3856 3218 4088 7310 0 0 7738 4600 4739 7143 5226 4437 3711 3584 7270 44310 0 21426 13790
3 29 1608 4815 6105 5899 8817 0 0 0 45523 1725 2413 2699 8708 11731 11565 12116
46 2228 2228 2228 4456 12202 17798 14108 11726 10756 11270 13508 1114 0 0 0 5532 15782 12940 8048 5344 5980 10890 0 0 4456 12445 3820 7800 11140 7706 5256 5104 10516 15160 35548 0 32807
13122 20 114 3588 7146 8328 12446 44597 0 0 0 47454 1494 5034 6354 14120 16100 16848
47 6272 7450 4599 3149 7428 18456 22909 18202 15851 14945 17279 6272 2680 0 0 0 9717 20928 14274 8485 7491 13108 5883 0 5086 8433 12138 3130 9808 11132 6433 5341 11280 5883 5105 25661 0
33509 11035 448 651 4516 7474 12084 24381 48512 0 0 0 41090 1477 7165 8709 13769 15269
48 14467 17090 15992 8665 5454 10566 21936 25687 21294 18737 20212 11169 9020 5686 0 0 0 11497 19758 12669 9155 14187 9591 3866 2744 9813 9941 11142 3721 9108 7617 5296 10733 9243 2572 10810 24108
0 29486 12075 1005 1571 5004 9863 12477 10615 49301 0 0 0 40438 2380 7109 8009 10669
49 20247 20393 25308 21688 11319 6762 11319 21688 25308 20393 20247 13815 10828 14498 9421 0 0 0 9421 14498 10828 13815 10467 5708 6189 4551 11169 10290 11169 4551 6189 5708 10467 8867 3550 1538 13634
26073 0 26073 13634 1538 3550 8867 8339 7536 4863 44880 0 0 0 44880 4863 7536 8339
50 20212 18737 21294 25687 21936 10566 5454 8665 15992 17090 14467 14187 9155 12669 19758 11497 0 0 0 5686 9020 11169 10733 5296 7617 9108 3721 11142 9941 9813 2744 3866 9591 9863 5004 1571 1005
12075 29486 0 24108 10810 2572 9243 10669 8009 7109 2380 40438 0 0 0 49301 10615 12477
51 17279 14945 15851 18202 22909 18456 7428 3149 4599 7450 6272 13108 7491 8485 14274 20928 9717 0 0 0 2680 6272 11280 5341 6433 11132 9808 3130 12138 8433 5086 0 5883 12084 7474 4516 651
448 11035 33509 0 25661 5105 5883 15269 13769 8709 7165 1477 41090 0 0 0 48512 24381
52 13508 11270 10756 11726 14108 17798 12202 4456 2228 2228 2228 10890 5980 5344 8048 12940 15782 5532 0 0 0 1114 10516 5104 5256 7706 11140 7800 3820 12445 4456 0 0 12446 8328 7146 3588
114 20 13122 32807 0 35548 15160 16848 16100 14120 6354 5034 1494 47454 0 0 0 44597
53 8949 7588 6669 6407 7426 8673 9768 6145 3294 3294 3294 7310 4088 3218 3856 5830 7974 7632 2623 0 0 0 7270 3584 3711 4437 5226 7143 4739 4600 7738 0 0 8817 5899 6105 4815
1608 29 3 13790 21426 0 44310 12116 11565 11731 8708 2699 2413 1725 45523 0 0 0
54 48103 43512 43501 41155 36527 29142 20216 17732 22228 32757 46848 36603 22555 22657 25841 24698 17903 10306 8951 12329 21977 47495 32534 15995 17373 22373 22586 20985 20118 16488 6288 8015 58119 35671 21954 19557 18622
18528 22273 29007 28487 13666 2 0 46133 41863 38961 32807 28890 30935 40806 46950 59471 0 0
Sum of all rows = 4(3*0 + 1*2 + 1*6288 + 1*8015 + 1*8951 + 1*10306 + 1*12329 + 1*13666 + 1*15995 + 1*16488 + 1*17373 + 1*17732 + 1*17903 + 1*18528 + 1*18622 + 1*19557 + 1*20118 + 1*20216 + 1*20985 + 1*21954 +
1*21977 + 1*22228 + 1*22273 + 1*22373 + 1*22555 + 1*22586 + 1*22657 + 1*24698 + 1*25841 + 1*28487 + 1*28890 + 1*29007 + 1*29142 + 1*30935 + 1*32534 + 1*32757 + 1*32807 + 1*35671 + 1*36527 +
1*36603 + 1*38961 + 1*40806 + 1*41155 + 1*41863 + 1*43501 + 1*43512 + 1*46133 + 1*46848 + 1*46950 + 1*47495 + 1*48103 + 1*58119 + 1*59471) +
4(9*0 + 1*3 + 1*29 + 1*1608 + 1*1725 + 1*2413 + 1*2623 + 1*2699 + 1*3218 + 3*3294 + 1*3584 + 1*3711 + 1*3856 + 1*4088 + 1*4437 + 1*4600 + 1*4739 + 1*4815 + 1*5226 + 1*5830 + 1*5899 + 1*6105 +
1*6145 + 1*6407 + 1*6669 + 1*7143 + 1*7270 + 1*7310 + 1*7426 + 1*7588 + 1*7632 + 1*7738 + 1*7974 + 1*8673 + 1*8708 + 1*8817 + 1*8949 + 1*9768 + 1*11565 + 1*11731 + 1*12116 + 1*13790 +
1*21426 + 1*44310 + 1*45523) +
4(9*0 + 1*20 + 1*114 + 1*1114 + 1*1494 + 3*2228 + 1*3588 + 1*3820 + 2*4456 + 1*5034 + 1*5104 + 1*5256 + 1*5344 + 1*5532 + 1*5980 + 1*6354 + 1*7146 + 1*7706 + 1*7800 + 1*8048 + 1*8328 + 1*10516 +
1*10756 + 1*10890 + 1*11140 + 1*11270 + 1*11726 + 1*12202 + 1*12445 + 1*12446 + 1*12940 + 1*13122 + 1*13508 + 1*14108 + 1*14120 + 1*15160 + 1*15782 + 1*16100 + 1*16848 + 1*17798 + 1*32807 +
1*35548 + 1*44597 + 1*47454) +
4(8*0 + 1*448 + 1*651 + 1*1477 + 1*2680 + 1*3130 + 1*3149 + 1*4516 + 1*4599 + 1*5086 + 1*5105 + 1*5341 + 2*5883 + 2*6272 + 1*6433 + 1*7165 + 1*7428 + 1*7450 + 1*7474 + 1*7491 + 1*8433 + 1*8485 +
1*8709 + 1*9717 + 1*9808 + 1*11035 + 1*11132 + 1*11280 + 1*12084 + 1*12138 + 1*13108 + 1*13769 + 1*14274 + 1*14945 + 1*15269 + 1*15851 + 1*17279 + 1*18202 + 1*18456 + 1*20928 + 1*22909 +
1*24381 + 1*25661 + 1*33509 + 1*41090 + 1*48512) +
4(7*0 + 1*1005 + 1*1571 + 1*2380 + 1*2572 + 1*2744 + 1*3721 + 1*3866 + 1*5004 + 1*5296 + 1*5454 + 1*5686 + 1*7109 + 1*7617 + 1*8009 + 1*8665 + 1*9020 + 1*9108 + 1*9155 + 1*9243 + 1*9591 +
1*9813 + 1*9863 + 1*9941 + 1*10566 + 1*10615 + 1*10669 + 1*10733 + 1*10810 + 1*11142 + 1*11169 + 1*11497 + 1*12075 + 1*12477 + 1*12669 + 1*14187 + 1*14467 + 1*15992 + 1*17090 + 1*18737 +
1*19758 + 1*20212 + 1*21294 + 1*21936 + 1*24108 + 1*25687 + 1*29486 + 1*40438 + 1*49301) +
2(7*0 + 2*1538 + 2*3550 + 2*4551 + 2*4863 + 2*5708 + 2*6189 + 1*6762 + 2*7536 + 2*8339 + 2*8867 + 2*9421 + 1*10290 + 2*10467 + 2*10828 + 2*11169 + 2*11319 + 2*13634 + 2*13815 + 2*14498 +
2*20247 + 2*20393 + 2*21688 + 2*25308 + 2*26073 + 2*44880) +
4(9*0 + 1*1 + 1*3 + 1*6 + 1*215 + 1*604 + 1*681 + 1*755 + 1*785 + 1*786 + 1*827 + 1*895 + 1*910 + 1*984 + 1*1009 + 1*1019 + 1*1038 + 1*1089 + 1*1104 + 1*1281 + 1*1379 + 1*1429 + 1*1440 +
1*1450 + 1*1587 + 1*1594 + 1*1638 + 1*1675 + 1*1718 + 1*1733 + 1*1765 + 1*1774 + 1*1906 + 1*1917 + 1*1988 + 1*2161 + 2*2293 + 1*2509 + 1*2603 + 1*2692 + 1*2698 + 1*2754 + 1*19195 + 1*19948 +
1*41835 + 1*44310) +
4(53*0 + 1*20388 + 1*23693) +
4(14*0 + 1*19 + 1*531 + 1*1087 + 1*1195 + 1*1616 + 1*1798 + 1*1860 + 1*1959 + 1*2064 + 1*2086 + 1*2127 + 1*2376 + 1*2441 + 1*2486 + 1*2541 + 1*2617 + 1*2821 + 1*3222 + 1*3318 + 1*3530 + 1*3618 +
1*3767 + 1*3971 + 1*3979 + 1*3990 + 1*4081 + 1*4640 + 1*4659 + 1*4748 + 1*4928 + 1*4967 + 1*5337 + 1*5915 + 1*6044 + 1*7761 + 1*7981 + 1*13139 + 2*15340 + 1*15985 + 1*17026) +
4(13*0 + 1*114 + 1*986 + 1*1605 + 1*2322 + 1*2650 + 4*2654 + 1*3128 + 1*3718 + 1*3792 + 1*4088 + 1*4416 + 1*4588 + 1*4796 + 1*4854 + 1*5206 + 1*6114 + 1*6248 + 1*6328 + 1*6366 + 1*6374 +
1*6806 + 1*7450 + 1*7720 + 1*7730 + 1*7740 + 1*7796 + 1*9284 + 1*9620 + 1*10324 + 1*10648 + 1*11106 + 1*11244 + 1*13364 + 1*13898 + 1*14100 + 1*14384 + 1*14745 + 1*16063 + 1*22634) +
4(13*0 + 1*381 + 1*922 + 1*1409 + 1*2710 + 1*2713 + 1*2766 + 1*3089 + 1*3414 + 1*3450 + 1*3654 + 1*3892 + 1*4498 + 1*4964 + 1*5038 + 1*5195 + 1*5309 + 1*5379 + 1*5420 + 1*6052 + 1*6073 +
1*6342 + 1*6555 + 1*6684 + 1*6732 + 1*6772 + 1*7002 + 1*8019 + 1*8034 + 1*8174 + 1*9262 + 1*9394 + 1*9742 + 1*9801 + 1*10294 + 1*12647 + 1*13314 + 1*13502 + 1*16257 + 1*17150 + 1*17382 +
1*18208 + 1*23635) +
2(13*0 + 2*1020 + 2*1248 + 2*2968 + 2*3024 + 2*4472 + 4*5280 + 2*5456 + 2*5492 + 2*6160 + 2*6216 + 2*6380 + 2*6712 + 2*6752 + 2*7904 + 2*8544 + 2*11280 + 2*12168 + 2*13400 + 2*15752 + 2*21158) +
2(49*0 + 2*13808 + 2*37501 + 2*43328) +
2(45*0 + 2*2805 + 4*5259 + 2*7963 + 2*14901) +
2(5*0 + 2*2692 + 1*3152 + 2*3576 + 2*4276 + 1*5152 + 2*5442 + 1*5552 + 2*6100 + 2*6352 + 2*6828 + 1*6928 + 2*6952 + 2*7164 + 2*7324 + 2*7516 + 2*9656 + 1*10456 + 2*10556 + 2*10972 + 2*11616 +
2*12272 + 2*13352 + 2*13752 + 2*13832 + 2*15160 + 2*16706 + 2*17060 + 1*20288) +
2(5*0 + 1*4650 + 2*5128 + 2*5183 + 2*6483 + 2*7083 + 1*7700 + 1*8240 + 2*9165 + 2*9314 + 1*9612 + 1*10260 + 2*10433 + 2*10509 + 2*10678 + 2*10901 + 2*11152 + 2*12273 + 1*12584 + 1*12720 +
2*13335 + 2*13815 + 1*15566 + 2*16613 + 2*17283 + 2*18465 + 2*19172 + 2*20470 + 2*20493 + 2*22578) +
2(5*0 + 2*4524 + 1*4572 + 1*4656 + 2*5464 + 2*5576 + 2*5812 + 2*6910 + 1*7412 + 1*7524 + 2*8964 + 2*9122 + 1*9376 + 2*9554 + 2*10100 + 2*10410 + 2*10586 + 2*11416 + 2*11560 + 1*12036 + 2*12984 +
2*13398 + 2*13984 + 1*14948 + 1*15056 + 2*16652 + 2*18466 + 2*20276 + 2*20628 + 2*21810) +
1(5*0 + 2*3932 + 4*4094 + 4*4892 + 2*6576 + 4*6734 + 2*8556 + 4*9468 + 4*9840 + 4*11310 + 4*12312 + 2*13020 + 2*13400 + 4*14908 + 4*18120 + 4*19580)
= 5793972 + 1463072 + 2066644 + 2259588 + 2414192 + 1253628 + 737104 + 176324 + 795640 + 1219860 + 1284920 + 626664 + 378548 + 144748 + 939680 + 1244768 + 1143944 + 536000
= 24479296
Value repetition frequencies = 4(52*1 + 1*3) +
4(43*1 + 1*3 + 1*9) +
4(41*1 + 1*2 + 1*3 + 1*9) +
4(43*1 + 2*2 + 1*8) +
4(48*1 + 1*7) +
2(2*1 + 23*2 + 1*7) +
4(44*1 + 1*2 + 1*9) +
4(2*1 + 1*53) +
4(39*1 + 1*2 + 1*14) +
4(38*1 + 1*4 + 1*13) +
4(42*1 + 1*13) +
2(19*2 + 1*4 + 1*13) +
2(3*2 + 1*49) +
2(3*2 + 1*4 + 1*45) +
2(6*1 + 22*2 + 1*5) +
2(8*1 + 21*2 + 1*5) +
2(8*1 + 21*2 + 1*5) +
1(5*2 + 10*4 + 1*5)
= 3025
Number of distinct row element sets = 18
Number of rows = 1*1 + 7*2 + 10*4
= 55
Number of distinct values = 542
Distinct values 0 1 2 3 6 19 20 29 114 215 381 448 531 604 651 681 755 785 786 827
Frequency 815 4 4 8 4 4 4 4 8 4 4 4 4 4 4 4 4 4 4 4
Distinct values 895 910 922 984 986 1005 1009 1019 1020 1038 1087 1089 1104 1114 1195 1248 1281 1379 1409 1429
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 1440 1450 1477 1494 1538 1571 1587 1594 1605 1608 1616 1638 1675 1718 1725 1733 1765 1774 1798 1860
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 1906 1917 1959 1988 2064 2086 2127 2161 2228 2293 2322 2376 2380 2413 2441 2486 2509 2541 2572 2603
Frequency 4 4 4 4 4 4 4 4 12 8 4 4 4 4 4 4 4 4 4 4
Distinct values 2617 2623 2650 2654 2680 2692 2698 2699 2710 2713 2744 2754 2766 2805 2821 2968 3024 3089 3128 3130
Frequency 4 4 4 16 4 8 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 3149 3152 3218 3222 3294 3318 3414 3450 3530 3550 3576 3584 3588 3618 3654 3711 3718 3721 3767 3792
Frequency 4 2 4 4 12 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 3820 3856 3866 3892 3932 3971 3979 3990 4081 4088 4094 4276 4416 4437 4456 4472 4498 4516 4524 4551
Frequency 4 4 4 4 2 4 4 4 4 8 4 4 4 4 8 4 4 4 4 4
Distinct values 4572 4588 4599 4600 4640 4650 4656 4659 4739 4748 4796 4815 4854 4863 4892 4928 4964 4967 5004 5034
Frequency 2 4 4 4 4 2 2 4 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 5038 5086 5104 5105 5128 5152 5183 5195 5206 5226 5256 5259 5280 5296 5309 5337 5341 5344 5379 5420
Frequency 4 4 4 4 4 2 4 4 4 4 4 8 8 4 4 4 4 4 4 4
Distinct values 5442 5454 5456 5464 5492 5532 5552 5576 5686 5708 5812 5830 5883 5899 5915 5980 6044 6052 6073 6100
Frequency 4 4 4 4 4 4 2 4 4 4 4 4 8 4 4 4 4 4 4 4
Distinct values 6105 6114 6145 6160 6189 6216 6248 6272 6288 6328 6342 6352 6354 6366 6374 6380 6407 6433 6483 6555
Frequency 4 4 4 4 4 4 4 8 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 6576 6669 6684 6712 6732 6734 6752 6762 6772 6806 6828 6910 6928 6952 7002 7083 7109 7143 7146 7164
Frequency 2 4 4 4 4 4 4 2 4 4 4 4 2 4 4 4 4 4 4 4
Distinct values 7165 7270 7310 7324 7412 7426 7428 7450 7474 7491 7516 7524 7536 7588 7617 7632 7700 7706 7720 7730
Frequency 4 4 4 4 2 4 4 8 4 4 4 2 4 4 4 4 2 4 4 4
Distinct values 7738 7740 7761 7796 7800 7904 7963 7974 7981 8009 8015 8019 8034 8048 8174 8240 8328 8339 8433 8485
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 2 4 4 4 4
Distinct values 8544 8556 8665 8673 8708 8709 8817 8867 8949 8951 8964 9020 9108 9122 9155 9165 9243 9262 9284 9314
Frequency 4 2 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 9376 9394 9421 9468 9554 9591 9612 9620 9656 9717 9742 9768 9801 9808 9813 9840 9863 9941 10100 10260
Frequency 2 4 4 4 4 4 2 4 4 4 4 4 4 4 4 4 4 4 4 2
Distinct values 10290 10294 10306 10324 10410 10433 10456 10467 10509 10516 10556 10566 10586 10615 10648 10669 10678 10733 10756 10810
Frequency 2 4 4 4 4 4 2 4 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 10828 10890 10901 10972 11035 11106 11132 11140 11142 11152 11169 11244 11270 11280 11310 11319 11416 11497 11560 11565
Frequency 4 4 4 4 4 4 4 4 4 4 8 4 4 8 4 4 4 4 4 4
Distinct values 11616 11726 11731 12036 12075 12084 12116 12138 12168 12202 12272 12273 12312 12329 12445 12446 12477 12584 12647 12669
Frequency 4 4 4 2 4 4 4 4 4 4 4 4 4 4 4 4 4 2 4 4
Distinct values 12720 12940 12984 13020 13108 13122 13139 13314 13335 13352 13364 13398 13400 13502 13508 13634 13666 13752 13769 13790
Frequency 2 4 4 2 4 4 4 4 4 4 4 4 6 4 4 4 4 4 4 4
Distinct values 13808 13815 13832 13898 13984 14100 14108 14120 14187 14274 14384 14467 14498 14745 14901 14908 14945 14948 15056 15160
Frequency 4 8 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 2 2 8
Distinct values 15269 15340 15566 15752 15782 15851 15985 15992 15995 16063 16100 16257 16488 16613 16652 16706 16848 17026 17060 17090
Frequency 4 8 2 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 17150 17279 17283 17373 17382 17732 17798 17903 18120 18202 18208 18456 18465 18466 18528 18622 18737 19172 19195 19557
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 19580 19758 19948 20118 20212 20216 20247 20276 20288 20388 20393 20470 20493 20628 20928 20985 21158 21294 21426 21688
Frequency 4 4 4 4 4 4 4 4 2 4 4 4 4 4 4 4 4 4 4 4
Distinct values 21810 21936 21954 21977 22228 22273 22373 22555 22578 22586 22634 22657 22909 23635 23693 24108 24381 24698 25308 25661
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 25687 25841 26073 28487 28890 29007 29142 29486 30935 32534 32757 32807 33509 35548 35671 36527 36603 37501 38961 40438
Frequency 4 4 4 4 4 4 4 4 4 4 4 8 4 4 4 4 4 4 4 4
Distinct values 40806 41090 41155 41835 41863 43328 43501 43512 44310 44597 44880 45523 46133 46848 46950 47454 47495 48103 48512 49301
Frequency 4 4 4 4 4 4 4 4 8 4 4 4 4 4 4 4 4 4 4 4
Distinct values 58119 59471
Frequency 4 4
Sum of distinct value frequencies = 28*2 + 491*4 + 1*6 + 18*8 + 2*12 + 1*16 + 1*815
= 3025
Number of SN-EN pairs for which the number of CNSAPs is greater than zero = 4*2 + 2*6 + 2*10 + 4*41 + 10*42 + 12*46 + 4*47 + 6*48 + 7*50 + 4*52
= 2210
Number of SN-EN pairs, with SN != EN, for which the number of CNSAPs equals zero = 760
Number of possible SN-EN pairs with SN != EN = 54*55
= 2970
a = 12, b = 5
L C
3 8
4 16
5 40
6 88
7 236
8 376
9 856
10 1380
11 3492
12 5284
13 13916
14 21052
15 53320
16 80296
17 176384
18 258040
19 474712
20 657152
21 1051720
22 1392524
23 2177972
24 2688352
25 4045468
26 4456652
27 6542396
28 6220144
29 9296004
30 7551900
31 11563964
32 7460408
33 10193748
34 4769140
35 3517136
36 1215380
37 457040
38 66628
39 3052
40 12
Total 86416288
Number of times each node is the starting node (SN) in a CNSAP of each length (L)
SN 0 1 2 3 4 5 6 7 8 9 10 11
12 13 14 15 16 17 18 19 20 21 22 23
24 25 26 27 28 29 30 31 32 33 34 35
36 37 38 39 40 41 42 43 44 45 46 47
48 49 50 51 52 53 54 55 56 57 58 59
L
3 0 0 0 0 0 0 0 0 0 0 0 0
0 2 0 0 0 0 0 0 0 0 2 0
0 0 0 0 0 0 0 0 0 0 0 0
0 2 0 0 0 0 0 0 0 0 2 0
0 0 0 0 0 0 0 0 0 0 0 0
4 0 0 0 0 0 0 0 0 0 0 0 0
0 0 2 0 0 0 0 0 0 2 0 0
0 4 0 0 0 0 0 0 0 0 4 0
0 0 2 0 0 0 0 0 0 2 0 0
0 0 0 0 0 0 0 0 0 0 0 0
5 0 0 1 0 0 0 0 0 0 1 0 0
0 2 0 2 0 0 0 0 2 0 2 0
2 0 8 0 0 0 0 0 0 8 0 2
0 2 0 2 0 0 0 0 2 0 2 0
0 0 1 0 0 0 0 0 0 1 0 0
6 0 2 0 3 0 0 0 0 3 0 2 0
3 0 6 0 2 0 0 2 0 6 0 3
0 0 0 12 0 0 0 0 12 0 0 0
3 0 6 0 2 0 0 2 0 6 0 3
0 2 0 3 0 0 0 0 3 0 2 0
7 5 1 9 0 5 0 0 5 0 9 1 5
1 4 2 16 2 4 4 2 16 2 4 1
2 2 0 0 16 0 0 16 0 0 2 2
1 4 2 16 2 4 4 2 16 2 4 1
5 1 9 0 5 0 0 5 0 9 1 5
8 0 8 0 23 0 7 7 0 23 0 8 0
4 2 3 2 29 4 4 29 2 3 2 4
0 0 0 4 0 20 20 0 4 0 0 0
4 2 3 2 29 4 4 29 2 3 2 4
0 8 0 23 0 7 7 0 23 0 8 0
9 13 5 14 4 53 13 13 53 4 14 5 13
5 7 4 11 8 52 52 8 11 4 7 5
6 2 0 0 18 24 24 18 0 0 2 6
5 7 4 11 8 52 52 8 11 4 7 5
13 5 14 4 53 13 13 53 4 14 5 13
10 6 16 4 21 17 97 97 17 21 4 16 6
10 4 6 6 29 77 77 29 6 6 4 10
2 2 2 8 32 58 58 32 8 2 2 2
10 4 6 6 29 77 77 29 6 6 4 10
6 16 4 21 17 97 97 17 21 4 16 6
11 33 23 39 38 59 184 184 59 38 39 23 33
20 31 24 41 134 109 109 134 41 24 31 20
26 14 8 44 44 140 140 44 44 8 14 26
20 31 24 41 134 109 109 134 41 24 31 20
33 23 39 38 59 184 184 59 38 39 23 33
12 23 39 36 57 273 110 110 273 57 36 39 23
32 21 26 160 67 229 229 67 160 26 21 32
14 14 50 28 260 130 130 260 28 50 14 14
32 21 26 160 67 229 229 67 160 26 21 32
23 39 36 57 273 110 110 273 57 36 39 23
13 85 115 145 489 225 348 348 225 489 145 115 85
86 112 274 145 570 256 256 570 145 274 112 86
110 110 52 474 128 384 384 128 474 52 110 110
86 112 274 145 570 256 256 570 145 274 112 86
85 115 145 489 225 348 348 225 489 145 115 85
14 105 118 622 207 612 352 352 612 207 622 118 105
124 327 123 953 206 440 440 206 953 123 327 124
132 98 748 106 828 236 236 828 106 748 98 132
124 327 123 953 206 440 440 206 953 123 327 124
105 118 622 207 612 352 352 612 207 622 118 105
15 280 1089 532 1608 826 1136 1136 826 1608 532 1089 280
608 401 1911 492 1257 718 718 1257 492 1911 401 608
416 1322 280 1892 396 638 638 396 1892 280 1322 416
608 401 1911 492 1257 718 718 1257 492 1911 401 608
280 1089 532 1608 826 1136 1136 826 1608 532 1089 280
16 1367 477 2666 719 1756 1047 1047 1756 719 2666 477 1367
495 3063 539 2377 629 891 891 629 2377 539 3063 495
1842 476 3740 488 1034 516 516 1034 488 3740 476 1842
495 3063 539 2377 629 891 891 629 2377 539 3063 495
1367 477 2666 719 1756 1047 1047 1756 719 2666 477 1367
17 1009 5441 1691 4773 2453 3079 3079 2453 4773 1691 5441 1009
5323 1394 5683 1554 2344 1824 1824 2344 1554 5683 1394 5323
1390 7474 1128 2774 1060 1230 1230 1060 2774 1128 7474 1390
5323 1394 5683 1554 2344 1824 1824 2344 1554 5683 1394 5323
1009 5441 1691 4773 2453 3079 3079 2453 4773 1691 5441 1009
18 9050 1892 8697 2286 3983 2593 2593 3983 2286 8697 1892 9050
1940 11241 2018 4187 1847 1877 1877 1847 4187 2018 11241 1940
12854 1874 6426 1670 1970 1004 1004 1970 1670 6426 1874 12854
1940 11241 2018 4187 1847 1877 1877 1847 4187 2018 11241 1940
9050 1892 8697 2286 3983 2593 2593 3983 2286 8697 1892 9050
19 3632 18986 4841 10090 6185 7213 7213 6185 10090 4841 18986 3632
22564 4552 10395 4256 5243 3671 3671 5243 4256 10395 4552 22564
4538 15810 3636 5412 2576 2128 2128 2576 5412 3636 15810 4538
22564 4552 10395 4256 5243 3671 3671 5243 4256 10395 4552 22564
3632 18986 4841 10090 6185 7213 7213 6185 10090 4841 18986 3632
20 34981 6733 17618 6322 9582 5588 5588 9582 6322 17618 6733 34981
7017 22163 6093 9240 4346 3890 3890 4346 9240 6093 22163 7017
32336 6352 12334 4412 4122 1874 1874 4122 4412 12334 6352 32336
7017 22163 6093 9240 4346 3890 3890 4346 9240 6093 22163 7017
34981 6733 17618 6322 9582 5588 5588 9582 6322 17618 6733 34981
21 12371 37226 13144 23637 13096 15694 15694 13096 23637 13144 37226 12371
47097 13456 21701 9762 11085 7540 7540 11085 9762 21701 13456 47097
14378 30296 9572 10910 5100 3986 3986 5100 10910 9572 30296 14378
47097 13456 21701 9762 11085 7540 7540 11085 9762 21701 13456 47097
12371 37226 13144 23637 13096 15694 15694 13096 23637 13144 37226 12371
22 60581 20522 42144 14401 21136 12245 12245 21136 14401 42144 20522 60581
22378 41002 14827 19247 7874 9741 9741 7874 19247 14827 41002 22378
62054 18236 22342 8362 7242 5830 5830 7242 8362 22342 18236 62054
22378 41002 14827 19247 7874 9741 9741 7874 19247 14827 41002 22378
60581 20522 42144 14401 21136 12245 12245 21136 14401 42144 20522 60581
23 37118 75087 31254 51430 26080 33947 33947 26080 51430 31254 75087 37118
80420 34126 41659 18010 23519 17636 17636 23519 18010 41659 34126 80420
41006 49736 19060 17696 9598 11318 11318 9598 17696 19060 49736 41006
80420 34126 41659 18010 23519 17636 17636 23519 18010 41659 34126 80420
37118 75087 31254 51430 26080 33947 33947 26080 51430 31254 75087 37118
24 110188 50955 78809 28756 45166 26799 26799 45166 28756 78809 50955 110188
59578 67985 26596 33234 16493 23187 23187 16493 33234 26596 67985 59578
90194 39704 31672 11242 19800 16072 16072 19800 11242 31672 39704 90194
59578 67985 26596 33234 16493 23187 23187 16493 33234 26596 67985 59578
110188 50955 78809 28756 45166 26799 26799 45166 28756 78809 50955 110188
25 91833 127799 63677 90324 56676 68992 68992 56676 90324 63677 127799 91833
125390 66506 61673 33404 49179 39414 39414 49179 33404 61673 66506 125390
94498 69624 25780 32376 20328 30394 30394 20328 32376 25780 69624 94498
125390 66506 61673 33404 49179 39414 39414 49179 33404 61673 66506 125390
91833 127799 63677 90324 56676 68992 68992 56676 90324 63677 127799 91833
26 166878 97046 115978 61447 75019 56014 56014 75019 61447 115978 97046 166878
118735 83850 39125 50684 34948 46336 46336 34948 50684 39125 83850 118735
138192 55798 38818 20694 44566 38138 38138 44566 20694 38818 55798 138192
118735 83850 39125 50684 34948 46336 46336 34948 50684 39125 83850 118735
166878 97046 115978 61447 75019 56014 56014 75019 61447 115978 97046 166878
27 169712 166654 123237 145187 118063 114644 114644 118063 145187 123237 166654 169712
179086 98100 82559 66420 77919 77710 77710 77919 66420 82559 98100 179086
153946 83560 35804 50650 44198 64458 64458 44198 50650 35804 83560 153946
179086 98100 82559 66420 77919 77710 77710 77919 66420 82559 98100 179086
169712 166654 123237 145187 118063 114644 114644 118063 145187 123237 166654 169712
28 211785 147141 142247 122985 104766 92266 92266 104766 122985 142247 147141 211785
158419 91515 63102 70777 69611 60130 60130 69611 70777 63102 91515 158419
156068 57352 46782 42162 65738 72482 72482 65738 42162 46782 57352 156068
158419 91515 63102 70777 69611 60130 60130 69611 70777 63102 91515 158419
211785 147141 142247 122985 104766 92266 92266 104766 122985 142247 147141 211785
29 224370 222339 220398 202501 204026 163353 163353 204026 202501 220398 222339 224370
198293 137995 106462 121171 117195 114352 114352 117195 121171 106462 137995 198293
189358 96826 44796 75782 87152 89178 89178 87152 75782 44796 96826 189358
198293 137995 106462 121171 117195 114352 114352 117195 121171 106462 137995 198293
224370 222339 220398 202501 204026 163353 163353 204026 202501 220398 222339 224370
30 217284 193476 178988 188670 127274 123971 123971 127274 188670 178988 193476 217284
167536 82715 85217 90201 101481 77021 77021 101481 90201 85217 82715 167536
129196 43898 56618 85216 101374 91980 91980 101374 85216 56618 43898 129196
167536 82715 85217 90201 101481 77021 77021 101481 90201 85217 82715 167536
217284 193476 178988 188670 127274 123971 123971 127274 188670 178988 193476 217284
31 264157 256626 299616 271161 262157 210511 210511 262157 271161 299616 256626 264157
207115 156196 125690 167246 153868 147020 147020 153868 167246 125690 156196 207115
229854 93478 55642 102174 131720 126388 126388 131720 102174 55642 93478 229854
207115 156196 125690 167246 153868 147020 147020 153868 167246 125690 156196 207115
264157 256626 299616 271161 262157 210511 210511 262157 271161 299616 256626 264157
32 186707 182011 167077 179047 143342 150291 150291 143342 179047 167077 182011 186707
150983 47955 80541 102203 104737 90660 90660 104737 102203 80541 47955 150983
81938 27438 72746 133168 132256 111550 111550 132256 133168 72746 27438 81938
150983 47955 80541 102203 104737 90660 90660 104737 102203 80541 47955 150983
186707 182011 167077 179047 143342 150291 150291 143342 179047 167077 182011 186707
33 241335 213102 251611 231556 216136 211363 211363 216136 231556 251611 213102 241335
176068 108588 102018 138239 143267 141789 141789 143267 138239 102018 108588 176068
220750 61052 66382 128942 142000 127604 127604 142000 128942 66382 61052 220750
176068 108588 102018 138239 143267 141789 141789 143267 138239 102018 108588 176068
241335 213102 251611 231556 216136 211363 211363 216136 231556 251611 213102 241335
34 117857 110086 82967 73282 97874 132303 132303 97874 73282 82967 110086 117857
80582 18430 49653 64466 63625 66316 66316 63625 64466 49653 18430 80582
22224 23252 80974 131198 117718 94322 94322 117718 131198 80974 23252 22224
80582 18430 49653 64466 63625 66316 66316 63625 64466 49653 18430 80582
117857 110086 82967 73282 97874 132303 132303 97874 73282 82967 110086 117857
35 101149 80212 73678 55068 66519 99732 99732 66519 55068 73678 80212 101149
46246 23401 38937 41314 39108 46158 46158 39108 41314 38937 23401 46246
58712 9998 62044 89746 65746 49278 49278 65746 89746 62044 9998 58712
46246 23401 38937 41314 39108 46158 46158 39108 41314 38937 23401 46246
101149 80212 73678 55068 66519 99732 99732 66519 55068 73678 80212 101149
36 34933 34248 20636 17471 26205 41798 41798 26205 17471 20636 34248 34933
13117 1983 9580 9196 7830 9062 9062 7830 9196 9580 1983 13117
2138 6096 42080 51126 30280 23852 23852 30280 51126 42080 6096 2138
13117 1983 9580 9196 7830 9062 9062 7830 9196 9580 1983 13117
34933 34248 20636 17471 26205 41798 41798 26205 17471 20636 34248 34933
37 13323 9254 11226 6164 11745 13247 13247 11745 6164 11226 9254 13323
4563 976 5261 3368 4398 4835 4835 4398 3368 5261 976 4563
5490 364 16012 12910 9520 7504 7504 9520 12910 16012 364 5490
4563 976 5261 3368 4398 4835 4835 4398 3368 5261 976 4563
13323 9254 11226 6164 11745 13247 13247 11745 6164 11226 9254 13323
38 2983 1084 951 1472 2294 1216 1216 2294 1472 951 1084 2983
172 0 538 487 437 626 626 437 487 538 0 172
0 596 4842 836 384 2136 2136 384 836 4842 596 0
172 0 538 487 437 626 626 437 487 538 0 172
2983 1084 951 1472 2294 1216 1216 2294 1472 951 1084 2983
39 110 116 64 0 143 67 67 143 0 64 116 110
0 0 0 8 12 26 26 12 8 0 0 0
0 0 250 24 0 160 160 0 24 250 0 0
0 0 0 8 12 26 26 12 8 0 0 0
110 116 64 0 143 67 67 143 0 64 116 110
40 0 2 0 0 0 0 0 0 0 0 2 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 2 2 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 2 0 0 0 0 0 0 0 0 2 0
Total 2315263 2059931 1954617 1791199 1643746 1590220 1590220 1643746 1791199 1954617 2059931 2315263
1874010 1118105 982248 1062879 1043299 993601 993601 1043299 1062879 982248 1118105 1874010
1743666 800858 760628 1022538 1047204 975014 975014 1047204 1022538 760628 800858 1743666
1874010 1118105 982248 1062879 1043299 993601 993601 1043299 1062879 982248 1118105 1874010
2315263 2059931 1954617 1791199 1643746 1590220 1590220 1643746 1791199 1954617 2059931 2315263
Grand total = 2*760628 + 2*800858 + 2*975014 + 4*982248 + 4*993601 + 2*1022538 + 4*1043299 + 2*1047204 + 4*1062879 + 4*1118105 + 4*1590220 + 4*1643746 + 2*1743666 + 4*1791199 + 4*1874010 + 4*1954617 + 4*2059931 + 4*2315263
= 86416288
Number of times each node is the ending node (EN) in a CNSAP of each length (L)
EN 0 1 2 3 4 5 6 7 8 9 10 11
12 13 14 15 16 17 18 19 20 21 22 23
24 25 26 27 28 29 30 31 32 33 34 35
36 37 38 39 40 41 42 43 44 45 46 47
48 49 50 51 52 53 54 55 56 57 58 59
L
3 2 0 0 0 0 0 0 0 0 0 0 2
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
2 0 0 0 0 0 0 0 0 0 0 2
4 4 0 0 0 0 0 0 0 0 0 0 4
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
4 0 0 0 0 0 0 0 0 0 0 4
5 10 0 0 0 0 0 0 0 0 0 0 10
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
10 0 0 0 0 0 0 0 0 0 0 10
6 22 0 0 0 0 0 0 0 0 0 0 22
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
22 0 0 0 0 0 0 0 0 0 0 22
7 46 2 2 2 2 2 2 2 2 2 2 46
2 0 0 0 0 0 0 0 0 0 0 2
2 0 0 0 0 0 0 0 0 0 0 2
2 0 0 0 0 0 0 0 0 0 0 2
46 2 2 2 2 2 2 2 2 2 2 46
8 83 1 2 2 2 2 2 2 2 2 1 83
1 0 0 0 0 0 0 0 0 0 0 1
2 0 0 0 0 0 0 0 0 0 0 2
1 0 0 0 0 0 0 0 0 0 0 1
83 1 2 2 2 2 2 2 2 2 1 83
9 159 6 9 10 10 10 10 10 10 9 6 159
6 0 0 0 0 0 0 0 0 0 0 6
8 0 0 0 0 0 0 0 0 0 0 8
6 0 0 0 0 0 0 0 0 0 0 6
159 6 9 10 10 10 10 10 10 9 6 159
10 282 6 9 13 14 14 14 14 13 9 6 282
5 0 0 0 0 0 0 0 0 0 0 5
4 0 0 0 0 0 0 0 0 0 0 4
5 0 0 0 0 0 0 0 0 0 0 5
282 6 9 13 14 14 14 14 13 9 6 282
11 536 26 44 49 55 56 56 55 49 44 26 536
19 4 8 8 8 8 8 8 8 8 4 19
32 8 16 16 16 16 16 16 16 16 8 32
19 4 8 8 8 8 8 8 8 8 4 19
536 26 44 49 55 56 56 55 49 44 26 536
12 989 26 43 58 65 73 73 65 58 43 26 989
11 0 4 4 4 4 4 4 4 4 0 11
12 4 16 16 16 16 16 16 16 16 4 12
11 0 4 4 4 4 4 4 4 4 0 11
989 26 43 58 65 73 73 65 58 43 26 989
13 1961 100 175 216 241 254 254 241 216 175 100 1961
60 20 44 56 56 56 56 56 56 44 20 60
88 32 72 96 96 96 96 96 96 72 32 88
60 20 44 56 56 56 56 56 56 44 20 60
1961 100 175 216 241 254 254 241 216 175 100 1961
14 3746 100 177 236 264 292 292 264 236 177 100 3746
20 0 32 46 48 48 48 48 46 32 0 20
24 16 88 124 128 128 128 128 124 88 16 24
20 0 32 46 48 48 48 48 46 32 0 20
3746 100 177 236 264 292 292 264 236 177 100 3746
15 7382 348 623 836 949 973 973 949 836 623 348 7382
175 72 174 278 306 308 308 306 278 174 72 175
232 84 240 380 436 440 440 436 380 240 84 232
175 72 174 278 306 308 308 306 278 174 72 175
7382 348 623 836 949 973 973 949 836 623 348 7382
16 13808 398 683 922 999 1024 1024 999 922 683 398 13808
63 0 141 258 306 322 322 306 258 141 0 63
44 30 318 564 656 688 688 656 564 318 30 44
63 0 141 258 306 322 322 306 258 141 0 63
13808 398 683 922 999 1024 1024 999 922 683 398 13808
17 24869 1136 1950 2551 3022 3108 3108 3022 2551 1950 1136 24869
446 177 502 882 1150 1232 1232 1150 882 502 177 446
548 196 726 1232 1652 1788 1788 1652 1232 726 196 548
446 177 502 882 1150 1232 1232 1150 882 502 177 446
24869 1136 1950 2551 3022 3108 3108 3022 2551 1950 1136 24869
18 42442 1556 2447 2996 3236 3271 3271 3236 2996 2447 1556 42442
221 0 446 967 1317 1424 1424 1317 967 446 0 221
104 42 942 1954 2508 2824 2824 2508 1954 942 42 104
221 0 446 967 1317 1424 1424 1317 967 446 0 221
42442 1556 2447 2996 3236 3271 3271 3236 2996 2447 1556 42442
19 64298 3616 5653 6884 7818 8570 8570 7818 6884 5653 3616 64298
1060 357 1263 2484 3350 3955 3955 3350 2484 1263 357 1060
1200 414 2058 3838 5226 6004 6004 5226 3838 2058 414 1200
1060 357 1263 2484 3350 3955 3955 3350 2484 1263 357 1060
64298 3616 5653 6884 7818 8570 8570 7818 6884 5653 3616 64298
20 97605 5073 7626 8429 8884 9116 9116 8884 8429 7626 5073 97605
707 0 1357 2995 4346 4872 4872 4346 2995 1357 0 707
272 76 2864 6078 8118 9148 9148 8118 6078 2864 76 272
707 0 1357 2995 4346 4872 4872 4346 2995 1357 0 707
97605 5073 7626 8429 8884 9116 9116 8884 8429 7626 5073 97605
21 122189 10010 14807 17451 18770 20315 20315 18770 17451 14807 10010 122189
2598 674 3398 6618 9131 10600 10600 9131 6618 3398 674 2598
2560 880 6054 11326 15082 16836 16836 15082 11326 6054 880 2560
2598 674 3398 6618 9131 10600 10600 9131 6618 3398 674 2598
122189 10010 14807 17451 18770 20315 20315 18770 17451 14807 10010 122189
22 172605 12676 19913 21582 21970 21962 21962 21970 21582 19913 12676 172605
2164 0 4162 8576 11698 13333 13333 11698 8576 4162 0 2164
664 190 9112 17390 22590 25034 25034 22590 17390 9112 190 664
2164 0 4162 8576 11698 13333 13333 11698 8576 4162 0 2164
172605 12676 19913 21582 21970 21962 21962 21970 21582 19913 12676 172605
23 210720 22756 34513 41463 42831 43254 43254 42831 41463 34513 22756 210720
6571 1390 9267 17207 22456 24872 24872 22456 17207 9267 1390 6571
5644 1940 17100 30732 37996 40974 40974 37996 30732 17100 1940 5644
6571 1390 9267 17207 22456 24872 24872 22456 17207 9267 1390 6571
210720 22756 34513 41463 42831 43254 43254 42831 41463 34513 22756 210720
24 274543 25768 43467 47935 48976 46009 46009 48976 47935 43467 25768 274543
5394 0 10829 22092 26828 29655 29655 26828 22092 10829 0 5394
1536 486 25058 43546 53636 56922 56922 53636 43546 25058 486 1536
5394 0 10829 22092 26828 29655 29655 26828 22092 10829 0 5394
274543 25768 43467 47935 48976 46009 46009 48976 47935 43467 25768 274543
25 313757 44411 69355 87126 86474 84578 84578 86474 87126 69355 44411 313757
15172 3176 21693 39287 48509 50079 50079 48509 39287 21693 3176 15172
12940 4458 41160 72128 80196 84618 84618 80196 72128 41160 4458 12940
15172 3176 21693 39287 48509 50079 50079 48509 39287 21693 3176 15172
313757 44411 69355 87126 86474 84578 84578 86474 87126 69355 44411 313757
26 367455 44862 76947 86593 90822 84308 84308 90822 86593 76947 44862 367455
11123 0 21106 45881 52017 53257 53257 52017 45881 21106 0 11123
3468 1194 54924 89900 105634 104464 104464 105634 89900 54924 1194 3468
11123 0 21106 45881 52017 53257 53257 52017 45881 21106 0 11123
367455 44862 76947 86593 90822 84308 84308 90822 86593 76947 44862 367455
27 396822 77520 120469 150916 147963 146385 146385 147963 150916 120469 77520 396822
31880 7587 41591 73860 87837 83003 83003 87837 73860 41591 7587 31880
30124 10482 79096 137200 141368 141262 141262 141368 137200 79096 10482 30124
31880 7587 41591 73860 87837 83003 83003 87837 73860 41591 7587 31880
396822 77520 120469 150916 147963 146385 146385 147963 150916 120469 77520 396822
28 406833 67940 112641 128018 135214 130343 130343 135214 128018 112641 67940 406833
18931 0 34921 75450 82171 74098 74098 82171 75450 34921 0 18931
7824 2880 95668 154668 168388 147524 147524 168388 154668 95668 2880 7824
18931 0 34921 75450 82171 74098 74098 82171 75450 34921 0 18931
406833 67940 112641 128018 135214 130343 130343 135214 128018 112641 67940 406833
29 423984 124422 194803 217251 216013 217911 217911 216013 217251 194803 124422 423984
62896 18098 71017 115093 127842 117471 117471 127842 115093 71017 18098 62896
69482 24412 135444 210744 209528 184790 184790 209528 210744 135444 24412 69482
62896 18098 71017 115093 127842 117471 117471 127842 115093 71017 18098 62896
423984 124422 194803 217251 216013 217911 217911 216013 217251 194803 124422 423984
30 385028 88398 146045 165551 163845 175309 175309 163845 165551 146045 88398 385028
30964 0 54275 98205 99841 90608 90608 99841 98205 54275 0 30964
17306 6656 147804 223752 212368 171926 171926 212368 223752 147804 6656 17306
30964 0 54275 98205 99841 90608 90608 99841 98205 54275 0 30964
385028 88398 146045 165551 163845 175309 175309 163845 165551 146045 88398 385028
31 414431 180575 259120 262459 264308 274789 274789 264308 262459 259120 180575 414431
113502 38069 102237 148272 147599 141516 141516 147599 148272 102237 38069 113502
137928 49444 189226 258566 240572 212492 212492 240572 258566 189226 49444 137928
113502 38069 102237 148272 147599 141516 141516 147599 148272 102237 38069 113502
414431 180575 259120 262459 264308 274789 274789 264308 262459 259120 180575 414431
32 303844 97315 142968 156538 164461 193456 193456 164461 156538 142968 97315 303844
43702 0 64886 97595 94516 87091 87091 94516 97595 64886 0 43702
28550 13202 183588 248294 198234 165592 165592 198234 248294 183588 13202 28550
43702 0 64886 97595 94516 87091 87091 94516 97595 64886 0 43702
303844 97315 142968 156538 164461 193456 193456 164461 156538 142968 97315 303844
33 317281 189156 224739 213350 225247 246285 246285 225247 213350 224739 189156 317281
128896 47559 93340 123351 120719 119243 119243 120719 123351 93340 47559 128896
157964 55834 186224 225418 194486 178616 178616 194486 225418 186224 55834 157964
128896 47559 93340 123351 120719 119243 119243 120719 123351 93340 47559 128896
317281 189156 224739 213350 225247 246285 246285 225247 213350 224739 189156 317281
34 167788 76616 79568 83906 110377 140485 140485 110377 83906 79568 76616 167788
36339 0 44154 53678 53442 52267 52267 53442 53678 44154 0 36339
18492 15010 155358 167356 121904 109210 109210 121904 167356 155358 15010 18492
36339 0 44154 53678 53442 52267 52267 53442 53678 44154 0 36339
167788 76616 79568 83906 110377 140485 140485 110377 83906 79568 76616 167788
35 115456 72216 70289 59316 79154 98311 98311 79154 59316 70289 72216 115456
36473 9818 33839 33909 32981 34191 34191 32981 33909 33839 9818 36473
46450 13920 107412 100788 71686 66406 66406 71686 100788 107412 13920 46450
36473 9818 33839 33909 32981 34191 34191 32981 33909 33839 9818 36473
115456 72216 70289 59316 79154 98311 98311 79154 59316 70289 72216 115456
36 43148 25563 20892 19132 31590 37010 37010 31590 19132 20892 25563 43148
8283 0 9638 8364 8262 8612 8612 8262 8364 9638 0 8283
2256 5698 59388 43226 27012 29122 29122 27012 43226 59388 5698 2256
8283 0 9638 8364 8262 8612 8612 8262 8364 9638 0 8283
43148 25563 20892 19132 31590 37010 37010 31590 19132 20892 25563 43148
37 15192 7692 10398 6835 13210 11655 11655 13210 6835 10398 7692 15192
3494 871 4568 3494 4328 4759 4759 4328 3494 4568 871 3494
4798 908 20772 10882 8784 9384 9384 8784 10882 20772 908 4798
3494 871 4568 3494 4328 4759 4759 4328 3494 4568 871 3494
15192 7692 10398 6835 13210 11655 11655 13210 6835 10398 7692 15192
38 2975 1078 1015 1390 2362 1227 1227 2362 1390 1015 1078 2975
124 0 516 495 424 636 636 424 495 516 0 124
0 570 5068 676 324 2192 2192 324 676 5068 570 0
124 0 516 495 424 636 636 424 495 516 0 124
2975 1078 1015 1390 2362 1227 1227 2362 1390 1015 1078 2975
39 108 118 64 0 143 67 67 143 0 64 118 108
0 0 0 8 12 26 26 12 8 0 0 0
0 0 250 24 0 160 160 0 24 250 0 0
0 0 0 8 12 26 26 12 8 0 0 0
108 118 64 0 143 67 67 143 0 64 118 108
40 0 2 0 0 0 0 0 0 0 0 2 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 2 2 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 2 0 0 0 0 0 0 0 0 2 0
Total 4712403 1181488 1661456 1790016 1889291 2000424 2000424 1889291 1790016 1661456 1181488 4712403
561302 127872 629408 979413 1041504 1007546 1007546 1041504 979413 629408 127872 561302
550558 209066 1526046 2060914 1928640 1768674 1768674 1928640 2060914 1526046 209066 550558
561302 127872 629408 979413 1041504 1007546 1007546 1041504 979413 629408 127872 561302
4712403 1181488 1661456 1790016 1889291 2000424 2000424 1889291 1790016 1661456 1181488 4712403
Grand total = 4*127872 + 2*209066 + 2*550558 + 4*561302 + 4*629408 + 4*979413 + 4*1007546 + 4*1041504 + 4*1181488 + 2*1526046 + 4*1661456 + 2*1768674 + 4*1790016 + 4*1889291 + 2*1928640 + 4*2000424 + 2*2060914 + 4*4712403
= 86416288
Number of times each node (N) is present in a CNSAP of each length (L)
N 0 1 2 3 4 5 6 7 8 9 10 11
12 13 14 15 16 17 18 19 20 21 22 23
24 25 26 27 28 29 30 31 32 33 34 35
36 37 38 39 40 41 42 43 44 45 46 47
48 49 50 51 52 53 54 55 56 57 58 59
L
3 2 1 0 0 0 0 0 0 0 0 1 2
1 2 0 0 0 0 0 0 0 0 2 1
0 0 0 0 0 0 0 0 0 0 0 0
1 2 0 0 0 0 0 0 0 0 2 1
2 1 0 0 0 0 0 0 0 0 1 2
4 4 2 0 0 0 0 0 0 0 0 2 4
2 4 2 0 0 0 0 0 0 2 4 2
0 4 0 0 0 0 0 0 0 0 4 0
2 4 2 0 0 0 0 0 0 2 4 2
4 2 0 0 0 0 0 0 0 0 2 4
5 10 5 1 0 0 0 0 0 0 1 5 10
5 12 5 2 0 0 0 0 2 5 12 5
2 10 8 0 0 0 0 0 0 8 10 2
5 12 5 2 0 0 0 0 2 5 12 5
10 5 1 0 0 0 0 0 0 1 5 10
6 22 13 1 3 0 0 0 0 3 1 13 22
14 28 17 6 2 0 0 2 6 17 28 14
2 22 16 12 0 0 0 0 12 16 22 2
14 28 17 6 2 0 0 2 6 17 28 14
22 13 1 3 0 0 0 0 3 1 13 22
7 53 32 17 7 9 4 4 9 7 17 32 53
31 60 47 30 10 6 6 10 30 47 60 31
14 58 62 40 28 12 12 28 40 62 58 14
31 60 47 30 10 6 6 10 30 47 60 31
53 32 17 7 9 4 4 9 7 17 32 53
8 86 54 20 31 10 11 11 10 31 20 54 86
50 101 87 62 45 14 14 45 62 87 101 50
10 78 106 84 52 32 32 52 84 106 78 10
50 101 87 62 45 14 14 45 62 87 101 50
86 54 20 31 10 11 11 10 31 20 54 86
9 183 113 61 69 85 45 45 85 69 61 113 183
113 206 183 155 120 96 96 120 155 183 206 113
44 166 240 226 178 140 140 178 226 240 166 44
113 206 183 155 120 96 96 120 155 183 206 113
183 113 61 69 85 45 45 85 69 61 113 183
10 308 191 77 109 141 163 163 141 109 77 191 308
178 346 291 261 257 269 269 257 261 291 346 178
34 266 348 372 364 334 334 364 372 348 266 34
178 346 291 261 257 269 269 257 261 291 346 178
308 191 77 109 141 163 163 141 109 77 191 308
11 630 439 299 365 403 564 564 403 365 299 439 630
438 805 761 804 828 897 897 828 804 761 805 438
220 630 792 1008 994 1096 1096 994 1008 792 630 220
438 805 761 804 828 897 897 828 804 761 805 438
630 439 299 365 403 564 564 403 365 299 439 630
12 1083 691 377 548 869 921 921 869 548 377 691 1083
658 1312 1137 1261 1428 1698 1698 1428 1261 1137 1312 658
164 1010 1274 1438 1832 2020 2020 1832 1438 1274 1010 164
658 1312 1137 1261 1428 1698 1698 1428 1261 1137 1312 658
1083 691 377 548 869 921 921 869 548 377 691 1083
13 2364 1872 1572 2357 2616 2823 2823 2616 2357 1572 1872 2364
1740 3166 3208 3681 4514 4690 4690 4514 3681 3208 3166 1740
950 2628 3178 4172 4868 5452 5452 4868 4172 3178 2628 950
1740 3166 3208 3681 4514 4690 4690 4514 3681 3208 3166 1740
2364 1872 1572 2357 2616 2823 2823 2616 2357 1572 1872 2364
14 4159 2786 2373 3267 4338 4590 4590 4338 3267 2373 2786 4159
2618 5440 5124 6227 7098 7980 7980 7098 6227 5124 5440 2618
902 4334 5950 6712 8334 9132 9132 8334 6712 5950 4334 902
2618 5440 5124 6227 7098 7980 7980 7098 6227 5124 5440 2618
4159 2786 2373 3267 4338 4590 4590 4338 3267 2373 2786 4159
15 8980 8117 7702 11382 13181 14012 14012 13181 11382 7702 8117 8980
7004 13010 14390 16120 19512 20647 20647 19512 16120 14390 13010 7004
3932 11898 14488 18198 20996 22274 22274 20996 18198 14488 11898 3932
7004 13010 14390 16120 19512 20647 20647 19512 16120 14390 13010 7004
8980 8117 7702 11382 13181 14012 14012 13181 11382 7702 8117 8980
16 16597 12116 11767 15550 19757 21446 21446 19757 15550 11767 12116 16597
10692 23823 23780 27405 29770 32071 32071 29770 27405 23780 23823 10692
5562 19994 28476 31370 33298 34120 34120 33298 31370 28476 19994 5562
10692 23823 23780 27405 29770 32071 32071 29770 27405 23780 23823 10692
16597 12116 11767 15550 19757 21446 21446 19757 15550 11767 12116 16597
17 31062 30926 29822 43164 51398 56936 56936 51398 43164 29822 30926 31062
27579 50590 56215 60872 67418 73608 73608 67418 60872 56215 50590 27579
15968 50716 61726 68014 69698 73962 73962 69698 68014 61726 50716 15968
27579 50590 56215 60872 67418 73608 73608 67418 60872 56215 50590 27579
31062 30926 29822 43164 51398 56936 56936 51398 43164 29822 30926 31062
18 57958 46037 47108 60702 74333 81038 81038 74333 60702 47108 46037 57958
41223 89453 89830 97073 100910 104250 104250 100910 97073 89830 89453 41223
30702 83730 106530 110350 106952 104266 104266 106952 110350 106530 83730 30702
41223 89453 89830 97073 100910 104250 104250 100910 97073 89830 89453 41223
57958 46037 47108 60702 74333 81038 81038 74333 60702 47108 46037 57958
19 87651 98553 99925 135120 160090 177033 177033 160090 135120 99925 98553 87651
91261 159445 171625 181210 192513 200277 200277 192513 181210 171625 159445 91261
64420 167808 192350 195654 189780 190346 190346 189780 195654 192350 167808 64420
91261 159445 171625 181210 192513 200277 200277 192513 181210 171625 159445 91261
87651 98553 99925 135120 160090 177033 177033 160090 135120 99925 98553 87651
20 159666 144989 152743 189770 221659 232385 232385 221659 189770 152743 144989 159666
132359 256253 254144 265802 270058 269553 269553 270058 265802 254144 256253 132359
113242 253852 289326 283880 271246 261212 261212 271246 283880 289326 253852 113242
132359 256253 254144 265802 270058 269553 269553 270058 265802 254144 256253 132359
159666 144989 152743 189770 221659 232385 232385 221659 189770 152743 144989 159666
21 205918 257078 286850 365048 407015 424071 424071 407015 365048 286850 257078 205918
241441 393834 421260 439879 460108 449456 449456 460108 439879 421260 393834 241441
209568 416572 438876 435480 431646 407002 407002 431646 435480 438876 416572 209568
241441 393834 421260 439879 460108 449456 449456 460108 439879 421260 393834 241441
205918 257078 286850 365048 407015 424071 424071 407015 365048 286850 257078 205918
22 333104 372428 433443 501527 538091 534421 534421 538091 501527 433443 372428 333104
346378 593592 588541 598825 595129 590845 590845 595129 598825 588541 593592 346378
336786 598638 615146 585322 568204 561020 561020 568204 585322 615146 598638 336786
346378 593592 588541 598825 595129 590845 590845 595129 598825 588541 593592 346378
333104 372428 433443 501527 538091 534421 534421 538091 501527 433443 372428 333104
23 458380 643570 761836 907823 937785 942435 942435 937785 907823 761836 643570 458380
597373 909161 951922 971767 963292 944066 944066 963292 971767 951922 909161 597373
597798 948290 937916 909008 850932 823914 823914 850932 909008 937916 948290 597798
597373 909161 951922 971767 963292 944066 944066 963292 971767 951922 909161 597373
458380 643570 761836 907823 937785 942435 942435 937785 907823 761836 643570 458380
24 678918 886001 1057926 1154824 1162846 1117331 1117331 1162846 1154824 1057926 886001 678918
826920 1247661 1207708 1190412 1164649 1161962 1161962 1164649 1190412 1207708 1247661 826920
859432 1266698 1185362 1082426 1067690 1084300 1084300 1067690 1082426 1185362 1266698 859432
826920 1247661 1207708 1190412 1164649 1161962 1161962 1164649 1190412 1207708 1247661 826920
678918 886001 1057926 1154824 1162846 1117331 1117331 1162846 1154824 1057926 886001 678918
25 944870 1426314 1739788 1948068 1919555 1871581 1871581 1919555 1948068 1739788 1426314 944870
1335760 1856405 1892962 1858805 1819947 1807000 1807000 1819947 1858805 1892962 1856405 1335760
1451892 1916038 1756388 1591696 1490862 1519364 1519364 1490862 1591696 1756388 1916038 1451892
1335760 1856405 1892962 1858805 1819947 1807000 1807000 1819947 1858805 1892962 1856405 1335760
944870 1426314 1739788 1948068 1919555 1871581 1871581 1919555 1948068 1739788 1426314 944870
26 1222997 1749761 2089123 2202770 2128854 2009199 2009199 2128854 2202770 2089123 1749761 1222997
1686833 2219774 2082796 2009684 1977923 1987788 1987788 1977923 2009684 2082796 2219774 1686833
1862662 2249944 1893772 1667556 1717574 1809964 1809964 1717574 1667556 1893772 2249944 1862662
1686833 2219774 2082796 2009684 1977923 1987788 1987788 1977923 2009684 2082796 2219774 1686833
1222997 1749761 2089123 2202770 2128854 2009199 2009199 2128854 2202770 2089123 1749761 1222997
27 1686177 2670827 3352756 3591575 3444867 3255637 3255637 3444867 3591575 3352756 2670827 1686177
2576606 3274763 3214032 3020672 3017007 3041990 3041990 3017007 3020672 3214032 3274763 2576606
2948438 3352320 2750366 2264828 2269994 2442582 2442582 2269994 2264828 2750366 3352320 2948438
2576606 3274763 3214032 3020672 3017007 3041990 3041990 3017007 3020672 3214032 3274763 2576606
1686177 2670827 3352756 3591575 3444867 3255637 3255637 3444867 3591575 3352756 2670827 1686177
28 1872508 2831505 3395844 3500687 3269878 3035775 3035775 3269878 3500687 3395844 2831505 1872508
2819868 3297348 2984687 2837351 2856956 2870967 2870967 2856956 2837351 2984687 3297348 2819868
3227966 3284260 2449182 2110144 2326854 2536862 2536862 2326854 2110144 2449182 3284260 3227966
2819868 3297348 2984687 2837351 2856956 2870967 2870967 2856956 2837351 2984687 3297348 2819868
1872508 2831505 3395844 3500687 3269878 3035775 3035775 3269878 3500687 3395844 2831505 1872508
29 2666563 4468655 5568182 5724514 5322071 4887618 4887618 5322071 5724514 5568182 4468655 2666563
4358625 5114666 4553489 4329896 4422113 4479398 4479398 4422113 4329896 4553489 5114666 4358625
5174312 5114932 3366834 2808768 3108800 3426832 3426832 3108800 2808768 3366834 5114932 5174312
4358625 5114666 4553489 4329896 4422113 4479398 4479398 4422113 4329896 4553489 5114666 4358625
2666563 4468655 5568182 5724514 5322071 4887618 4887618 5322071 5724514 5568182 4468655 2666563
30 2567857 4032714 4762672 4730716 4256589 3917267 3917267 4256589 4730716 4762672 4032714 2567857
4089849 4192913 3571848 3504808 3600868 3576017 3576017 3600868 3504808 3571848 4192913 4089849
4778470 4004990 2548022 2448480 2854598 3035704 3035704 2854598 2448480 2548022 4004990 4778470
4089849 4192913 3571848 3504808 3600868 3576017 3576017 3600868 3504808 3571848 4192913 4089849
2567857 4032714 4762672 4730716 4256589 3917267 3917267 4256589 4730716 4762672 4032714 2567857
31 4014373 6553516 7946700 7829735 6961443 6297856 6297856 6961443 7829735 7946700 6553516 4014373
6810815 6490736 5419358 5440709 5661722 5731255 5731255 5661722 5440709 5419358 6490736 6810815
8256572 6082776 3291214 3135198 3871132 4288114 4288114 3871132 3135198 3291214 6082776 8256572
6810815 6490736 5419358 5440709 5661722 5731255 5731255 5661722 5440709 5419358 6490736 6810815
4014373 6553516 7946700 7829735 6961443 6297856 6297856 6961443 7829735 7946700 6553516 4014373
32 3025910 4607867 5365205 5106337 4467951 4087050 4087050 4467951 5106337 5365205 4607867 3025910
4895000 4011589 3416839 3506121 3631227 3613683 3613683 3631227 3506121 3416839 4011589 4895000
5796954 3604126 2129104 2398254 2901408 3067124 3067124 2901408 2398254 2129104 3604126 5796954
4895000 4011589 3416839 3506121 3631227 3613683 3613683 3631227 3506121 3416839 4011589 4895000
3025910 4607867 5365205 5106337 4467951 4087050 4087050 4467951 5106337 5365205 4607867 3025910
33 4521418 6710388 7967342 7371495 6352036 5795307 5795307 6352036 7371495 7967342 6710388 4521418
7476045 5130179 4575933 4810816 5088496 5163702 5163702 5088496 4810816 4575933 5130179 7476045
9117908 4309928 2323310 2807400 3666394 4045588 4045588 3666394 2807400 2323310 4309928 9117908
7476045 5130179 4575933 4810816 5088496 5163702 5163702 5088496 4810816 4575933 5130179 7476045
4521418 6710388 7967342 7371495 6352036 5795307 5795307 6352036 7371495 7967342 6710388 4521418
34 2341732 3357946 3829359 3430762 3016489 2859598 2859598 3016489 3430762 3829359 3357946 2341732
3672866 2307951 2107302 2256261 2368923 2388569 2388569 2368923 2256261 2107302 2307951 3672866
4361140 1925400 1238422 1676886 1971402 2026614 2026614 1971402 1676886 1238422 1925400 4361140
3672866 2307951 2107302 2256261 2368923 2388569 2388569 2368923 2256261 2107302 2307951 3672866
2341732 3357946 3829359 3430762 3016489 2859598 2859598 3016489 3430762 3829359 3357946 2341732
35 1878448 2653762 2968736 2397709 2229804 2385941 2385941 2229804 2397709 2968736 2653762 1878448
2809827 1589170 1634753 1732374 1775905 1767433 1767433 1775905 1732374 1634753 1589170 2809827
3355290 1240182 907292 1401228 1546818 1451346 1451346 1546818 1401228 907292 1240182 3355290
2809827 1589170 1634753 1732374 1775905 1767433 1767433 1775905 1732374 1634753 1589170 2809827
1878448 2653762 2968736 2397709 2229804 2385941 2385941 2229804 2397709 2968736 2653762 1878448
36 711745 987340 1061096 834656 790087 875396 875396 790087 834656 1061096 987340 711745
1005371 506739 528834 583249 593897 598848 598848 593897 583249 528834 506739 1005371
1172976 412264 390844 607296 599968 538976 538976 599968 607296 390844 412264 1172976
1005371 506739 528834 583249 593897 598848 598848 593897 583249 528834 506739 1005371
711745 987340 1061096 834656 790087 875396 875396 790087 834656 1061096 987340 711745
37 291838 401735 426180 282369 298603 374945 374945 298603 282369 426180 401735 291838
390242 167569 207173 201974 217778 212535 212535 217778 201974 207173 167569 390242
449482 122852 180154 284172 277414 195284 195284 277414 284172 180154 122852 449482
390242 167569 207173 201974 217778 212535 212535 217778 201974 207173 167569 390242
291838 401735 426180 282369 298603 374945 374945 298603 282369 426180 401735 291838
38 47910 61508 62954 39592 44391 57391 57391 44391 39592 62954 61508 47910
58754 19918 31326 28320 32086 30126 30126 32086 28320 31326 19918 58754
66132 15796 36626 44320 43276 31230 31230 43276 44320 36626 15796 66132
58754 19918 31326 28320 32086 30126 30126 32086 28320 31326 19918 58754
47910 61508 62954 39592 44391 57391 57391 44391 39592 62954 61508 47910
39 2396 2926 2786 1654 2476 2504 2504 2476 1654 2786 2926 2396
2862 686 1622 1164 1710 1408 1408 1710 1164 1622 686 2862
3052 380 2356 1948 1864 1526 1526 1864 1948 2356 380 3052
2862 686 1622 1164 1710 1408 1408 1710 1164 1622 686 2862
2396 2926 2786 1654 2476 2504 2504 2476 1654 2786 2926 2396
40 12 12 8 4 12 12 12 12 4 8 12 12
12 0 12 8 8 0 0 8 8 12 0 12
12 0 8 0 8 12 12 8 0 8 0 12
12 0 12 8 8 0 0 8 8 12 0 12
12 12 8 4 12 12 12 12 4 8 12 12
Total 29843892 45022790 53432651 52384309 48099732 45323306 45323306 48099732 52384309 53432651 45022790 29843892
46317413 43928710 40013243 39984066 40944227 41133104 41133104 40944227 39984066 40013243 43928710 46317413
54263010 41463590 29146064 28981940 32275458 33997756 33997756 32275458 28981940 29146064 41463590 54263010
46317413 43928710 40013243 39984066 40944227 41133104 41133104 40944227 39984066 40013243 43928710 46317413
29843892 45022790 53432651 52384309 48099732 45323306 45323306 48099732 52384309 53432651 45022790 29843892
Grand total = 2*28981940 + 2*29146064 + 4*29843892 + 2*32275458 + 2*33997756 + 4*39984066 + 4*40013243 + 4*40944227 + 4*41133104 + 2*41463590 + 4*43928710 + 4*45022790 + 4*45323306 + 4*46317413 + 4*48099732 + 4*52384309 +
4*53432651 + 2*54263010
= 2545965408
Number of CNSAPs for each starting node (SN) and ending node (EN) pair
SN 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59
EN
0 0 0 172793 137380 120467 91938 83260 90111 108895 127705 133539 146052 0 2 40164 83552 84052 63303 52597 55811 63152 65154 69579 111480 168762 23021 18433 48930 58631 58371 62392
69475 68680 53216 48956 99586 139048 64412 36311 26347 29928 50757 70154 78202 73213 64007 66657 109759 137431 95915 64912 51927 59703 85645 104042 112063 117735 124605 127786 142405
1 0 0 0 132205 4845 6896 7584 23772 32944 34660 32550 35295 128482 0 62601 41391 3 29 4425 14538 20545 18364 16648 26142 0 0 22986 14120 14156 19901 14240
13467 14539 11773 10961 22226 0 0 0 7711 22338 23238 17105 11680 9650 10749 13830 23221 9728 9728 9728 18315 29561 26640 22450 17976 18094 22354 25949 29155
2 129191 0 0 0 139436 4354 13674 17214 41090 51918 50590 53432 44310 103254 0 94535 38894 20 114 10528 24080 27364 25790 38916 0 0 13176 36809 11500 21760 31010
23370 20346 16604 15808 32104 3294 0 0 0 15738 44420 37152 24098 15702 13956 18238 32318 6588 6588 6588 13176 36271 53114 41352 31916 27162 29234 33822 39538
3 71029 139616 0 0 0 121201 4245 19939 25441 47912 53098 55780 17388 15160 75540 0 95409 30093 1178 1317 14398 24637 27436 41103 17388 0 14872 24446 35017 8230 27212
35234 25361 17600 16806 34566 18502 7890 0 0 0 26740 58179 41886 25356 17298 19646 35615 18502 21951 13364 9004 21258 52326 63029 46784 37981 35090 36959 44004
4 36573 31079 144500 0 0 0 117109 5342 22090 26520 40310 44718 27104 7439 31682 72374 0 85710 30559 2630 2975 13711 21820 35272 28234 11377 7950 29286 28557 30845 8811
28758 31641 18588 15571 32798 32950 26657 16426 0 0 0 33178 60236 39876 24288 21815 37953 42771 50569 46626 24642 15217 29221 59017 65292 51544 45704 43419 49957
5 24421 22133 14543 137189 0 0 0 126192 7935 20790 23218 31134 26154 10521 4418 42319 77440 0 80926 38907 3547 5118 14556 28739 30807 16752 18096 14382 33863 29365 31430
12585 26308 22020 15348 31181 40556 31800 41664 26278 0 0 0 32993 54547 35949 26485 41079 59328 59737 73382 61451 32289 20186 33392 62275 71728 60474 54110 58384
6 31134 23218 20790 7935 126192 0 0 0 137189 14543 22133 24421 28739 14556 5118 3547 38907 80926 0 77440 42319 4418 10521 26154 31181 15348 22020 26308 12585 31430 29365
33863 14382 18096 16752 30807 41079 26485 35949 54547 32993 0 0 0 26278 41664 31800 40556 58384 54110 60474 71728 62275 33392 20186 32289 61451 73382 59737 59328
7 44718 40310 26520 22090 5342 117109 0 0 0 144500 31079 36573 35272 21820 13711 2975 2630 30559 85710 0 72374 31682 7439 27104 32798 15571 18588 31641 28758 8811 30845
28557 29286 7950 11377 28234 37953 21815 24288 39876 60236 33178 0 0 0 16426 26657 32950 49957 43419 45704 51544 65292 59017 29221 15217 24642 46626 50569 42771
8 55780 53098 47912 25441 19939 4245 121201 0 0 0 139616 71029 41103 27436 24637 14398 1317 1178 30093 95409 0 75540 15160 17388 34566 16806 17600 25361 35234 27212 8230
35017 24446 14872 0 17388 35615 19646 17298 25356 41886 58179 26740 0 0 0 7890 18502 44004 36959 35090 37981 46784 63029 52326 21258 9004 13364 21951 18502
9 53432 50590 51918 41090 17214 13674 4354 139436 0 0 0 129191 38916 25790 27364 24080 10528 114 20 38894 94535 0 103254 44310 32104 15808 16604 20346 23370 31010 21760
11500 36809 13176 0 0 32318 18238 13956 15702 24098 37152 44420 15738 0 0 0 3294 39538 33822 29234 27162 31916 41352 53114 36271 13176 6588 6588 6588
10 35295 32550 34660 32944 23772 7584 6896 4845 132205 0 0 0 26142 16648 18364 20545 14538 4425 29 3 41391 62601 0 128482 22226 10961 11773 14539 13467 14240 19901
14156 14120 22986 0 0 23221 13830 10749 9650 11680 17105 23238 22338 7711 0 0 0 29155 25949 22354 18094 17976 22450 26640 29561 18315 9728 9728 9728
11 146052 133539 127705 108895 90111 83260 91938 120467 137380 172793 0 0 111480 69579 65154 63152 55811 52597 63303 84052 83552 40164 2 0 99586 48956 53216 68680 69475 62392 58371
58631 48930 18433 23021 168762 109759 66657 64007 73213 78202 70154 50757 29928 26347 36311 64412 139048 142405 127786 124605 117735 112063 104042 85645 59703 51927 64912 95915 137431
12 0 128482 0 0 5208 5344 4297 3851 4635 5988 6644 7270 0 0 0 0 4601 4115 2909 2257 2458 2976 3495 5622 0 58119 8013 2754 3203 2181 2712
3446 3544 2759 2525 5131 121087 6778 0 1 3 6 2916 4821 4733 3729 3530 5779 56075 6778 5013 1719 605 1937 5339 7069 7321 7092 6834 7598
13 0 0 58944 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 68928 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
14 45397 46672 0 49964 14095 5849 5158 6759 11654 15289 15555 16473 45397 0 0 0 22465 19 3259 3169 6527 7971 7991 12123 23693 38844 0 11466 7496 1481 7941
8183 7087 5378 4984 10166 0 0 0 0 0 8958 15136 10657 6468 5003 5914 10456 0 0 0 0 6873 17458 16828 12687 10256 10171 11094 12944
15 43945 41248 64606 0 47854 27820 13088 12124 15444 23662 27326 29162 23321 33267 0 0 0 39786 114 7930 7162 11738 14302 22086 7981 7981 18297 0 20658 11194 2350
15786 15294 10604 9468 19412 7981 0 0 0 0 0 21480 31514 20700 12410 12072 21128 7981 4805 0 0 0 17424 39432 35342 27900 23842 23324 27068
16 27002 19206 29478 66718 0 53870 31672 15394 14800 17425 22765 25861 17399 7796 36172 0 0 0 48720 381 8877 7779 12437 21301 12938 2654 9882 14764 0 22649 13934
3359 16229 12690 10468 21178 15592 7962 0 0 0 0 0 25862 34490 21329 16054 25906 18246 19336 9630 0 0 0 23004 48640 44656 37159 32200 35640
17 16424 14636 11926 23038 62417 0 59118 26808 13240 13812 14372 17584 14580 7896 2710 42978 0 0 0 48596 1020 7192 8272 16364 16602 8074 3450 14826 18562 0 21552
15808 4160 10600 9852 18908 21100 17992 13830 0 0 0 0 0 21472 26340 18296 25052 30096 32408 35138 16501 0 0 0 21780 46020 43644 35980 36520
18 17584 14372 13812 13240 26808 59118 0 62417 23038 11926 14636 16424 16364 8272 7192 1020 48596 0 0 0 42978 2710 7896 14580 18908 9852 10600 4160 15808 21552 0
18562 14826 3450 8074 16602 25052 18296 26340 21472 0 0 0 0 0 13830 17992 21100 36520 35980 43644 46020 21780 0 0 0 16501 35138 32408 30096
19 25861 22765 17425 14800 15394 31672 53870 0 66718 29478 19206 27002 21301 12437 7779 8877 381 48720 0 0 0 36172 7796 17399 21178 10468 12690 16229 3359 13934 22649
0 14764 9882 2654 12938 25906 16054 21329 34490 25862 0 0 0 0 0 7962 15592 35640 32200 37159 44656 48640 23004 0 0 0 9630 19336 18246
20 29162 27326 23662 15444 12124 13088 27820 47854 0 64606 41248 43945 22086 14302 11738 7162 7930 114 39786 0 0 0 33267 23321 19412 9468 10604 15294 15786 2350 11194
20658 0 18297 7981 7981 21128 12072 12410 20700 31514 21480 0 0 0 0 0 7981 27068 23324 23842 27900 35342 39432 17424 0 0 0 4805 7981
21 16473 15555 15289 11654 6759 5158 5849 14095 49964 0 46672 45397 12123 7991 7971 6527 3169 3259 19 22465 0 0 0 45397 10166 4984 5378 7087 8183 7941 1481
7496 11466 0 38844 23693 10456 5914 5003 6468 10657 15136 8958 0 0 0 0 0 12944 11094 10171 10256 12687 16828 17458 6873 0 0 0 0
22 0 0 0 0 0 0 0 0 0 58944 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 68928 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
23 7270 6644 5988 4635 3851 4297 5344 5208 0 0 128482 0 5622 3495 2976 2458 2257 2909 4115 4601 0 0 0 0 5131 2525 2759 3544 3446 2712 2181
3203 2754 8013 58119 0 5779 3530 3729 4733 4821 2916 6 3 1 0 6778 121087 7598 6834 7092 7321 7069 5339 1937 605 1719 5013 6778 56075
24 125793 40279 0 0 0 0 0 0 0 0 0 0 0 109207 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 109207 0 0 0 0 0 0 0 0 0 0 125793 40279 0 0 0 0 0 0 0 0 0 0
25 15006 15006 8021 0 0 0 0 0 0 0 0 0 43328 0 23172 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 43328 0 23172 0 0 0 0 0 0 0 0 0 15006 15006 8021 0 0 0 0 0 0 0 0 0
26 40320 48966 30566 17390 12232 22060 31312 33560 36760 40704 42052 46392 49962 28455 0 15930 7536 10100 19728 22112 22096 20836 21920 35576 59604 0 0 0 18344 8736 17704
21680 21944 17128 15752 32024 49962 28455 0 15930 7536 10100 19728 22112 22096 20836 21920 35576 40320 48966 30566 17390 12232 22060 31312 33560 36760 40704 42052 46392
27 54868 41036 48803 31541 27587 21592 35515 52813 56552 60602 62586 69079 39652 27204 30284 0 19055 14797 14691 33763 34207 31083 32607 52962 37808 30432 0 0 0 34936 12188
30472 32650 25550 23458 47662 39652 27204 30284 0 19055 14797 14691 33763 34207 31083 32607 52962 54868 41036 48803 31541 27587 21592 35515 52813 56552 60602 62586 69079
28 54915 40005 26400 33226 27337 32388 22566 37506 59134 61160 60546 66726 41715 17505 16005 31844 0 27764 17416 13916 34604 31608 31556 51096 35970 13950 27360 0 0 0 42328
12060 29424 24880 22780 46012 41715 17505 16005 31844 0 27764 17416 13916 34604 31608 31556 51096 54915 40005 26400 33226 27337 32388 22566 37506 59134 61160 60546 66726
29 55572 51328 34968 18910 27920 26254 30220 19362 35892 57172 55796 59890 42348 26828 11798 13668 32221 0 31810 15812 12096 28882 29134 45712 38072 18656 11244 36332 0 0 0
42420 12244 20492 20692 41336 42348 26828 11798 13668 32221 0 31810 15812 12096 28882 29134 45712 55572 51328 34968 18910 27920 26254 30220 19362 35892 57172 55796 59890
30 59890 55796 57172 35892 19362 30220 26254 27920 18910 34968 51328 55572 45712 29134 28882 12096 15812 31810 0 32221 13668 11798 26828 42348 41336 20692 20492 12244 42420 0 0
0 36332 11244 18656 38072 45712 29134 28882 12096 15812 31810 0 32221 13668 11798 26828 42348 59890 55796 57172 35892 19362 30220 26254 27920 18910 34968 51328 55572
31 66726 60546 61160 59134 37506 22566 32388 27337 33226 26400 40005 54915 51096 31556 31608 34604 13916 17416 27764 0 31844 16005 17505 41715 46012 22780 24880 29424 12060 42328 0
0 0 27360 13950 35970 51096 31556 31608 34604 13916 17416 27764 0 31844 16005 17505 41715 66726 60546 61160 59134 37506 22566 32388 27337 33226 26400 40005 54915
32 69079 62586 60602 56552 52813 35515 21592 27587 31541 48803 41036 54868 52962 32607 31083 34207 33763 14691 14797 19055 0 30284 27204 39652 47662 23458 25550 32650 30472 12188 34936
0 0 0 30432 37808 52962 32607 31083 34207 33763 14691 14797 19055 0 30284 27204 39652 69079 62586 60602 56552 52813 35515 21592 27587 31541 48803 41036 54868
33 46392 42052 40704 36760 33560 31312 22060 12232 17390 30566 48966 40320 35576 21920 20836 22096 22112 19728 10100 7536 15930 0 28455 49962 32024 15752 17128 21944 21680 17704 8736
18344 0 0 0 59604 35576 21920 20836 22096 22112 19728 10100 7536 15930 0 28455 49962 46392 42052 40704 36760 33560 31312 22060 12232 17390 30566 48966 40320
34 0 0 0 0 0 0 0 0 0 8021 15006 15006 0 0 0 0 0 0 0 0 0 23172 0 43328 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 23172 0 43328 0 0 0 0 0 0 0 0 0 8021 15006 15006
35 0 0 0 0 0 0 0 0 0 0 40279 125793 0 0 0 0 0 0 0 0 0 0 109207 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 109207 0 0 0 0 0 0 0 0 0 0 0 40279 125793
36 56075 6778 5013 1719 605 1937 5339 7069 7321 7092 6834 7598 121087 6778 0 1 3 6 2916 4821 4733 3729 3530 5779 0 58119 8013 2754 3203 2181 2712
3446 3544 2759 2525 5131 0 0 0 0 4601 4115 2909 2257 2458 2976 3495 5622 0 128482 0 0 5208 5344 4297 3851 4635 5988 6644 7270
37 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 68928 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 58944 0 0 0 0 0 0 0 0 0
38 0 0 0 0 6873 17458 16828 12687 10256 10171 11094 12944 0 0 0 0 0 8958 15136 10657 6468 5003 5914 10456 23693 38844 0 11466 7496 1481 7941
8183 7087 5378 4984 10166 45397 0 0 0 22465 19 3259 3169 6527 7971 7991 12123 45397 46672 0 49964 14095 5849 5158 6759 11654 15289 15555 16473
39 7981 4805 0 0 0 17424 39432 35342 27900 23842 23324 27068 7981 0 0 0 0 0 21480 31514 20700 12410 12072 21128 7981 7981 18297 0 20658 11194 2350
15786 15294 10604 9468 19412 23321 33267 0 0 0 39786 114 7930 7162 11738 14302 22086 43945 41248 64606 0 47854 27820 13088 12124 15444 23662 27326 29162
40 18246 19336 9630 0 0 0 23004 48640 44656 37159 32200 35640 15592 7962 0 0 0 0 0 25862 34490 21329 16054 25906 12938 2654 9882 14764 0 22649 13934
3359 16229 12690 10468 21178 17399 7796 36172 0 0 0 48720 381 8877 7779 12437 21301 27002 19206 29478 66718 0 53870 31672 15394 14800 17425 22765 25861
41 30096 32408 35138 16501 0 0 0 21780 46020 43644 35980 36520 21100 17992 13830 0 0 0 0 0 21472 26340 18296 25052 16602 8074 3450 14826 18562 0 21552
15808 4160 10600 9852 18908 14580 7896 2710 42978 0 0 0 48596 1020 7192 8272 16364 16424 14636 11926 23038 62417 0 59118 26808 13240 13812 14372 17584
42 36520 35980 43644 46020 21780 0 0 0 16501 35138 32408 30096 25052 18296 26340 21472 0 0 0 0 0 13830 17992 21100 18908 9852 10600 4160 15808 21552 0
18562 14826 3450 8074 16602 16364 8272 7192 1020 48596 0 0 0 42978 2710 7896 14580 17584 14372 13812 13240 26808 59118 0 62417 23038 11926 14636 16424
43 35640 32200 37159 44656 48640 23004 0 0 0 9630 19336 18246 25906 16054 21329 34490 25862 0 0 0 0 0 7962 15592 21178 10468 12690 16229 3359 13934 22649
0 14764 9882 2654 12938 21301 12437 7779 8877 381 48720 0 0 0 36172 7796 17399 25861 22765 17425 14800 15394 31672 53870 0 66718 29478 19206 27002
44 27068 23324 23842 27900 35342 39432 17424 0 0 0 4805 7981 21128 12072 12410 20700 31514 21480 0 0 0 0 0 7981 19412 9468 10604 15294 15786 2350 11194
20658 0 18297 7981 7981 22086 14302 11738 7162 7930 114 39786 0 0 0 33267 23321 29162 27326 23662 15444 12124 13088 27820 47854 0 64606 41248 43945
45 12944 11094 10171 10256 12687 16828 17458 6873 0 0 0 0 10456 5914 5003 6468 10657 15136 8958 0 0 0 0 0 10166 4984 5378 7087 8183 7941 1481
7496 11466 0 38844 23693 12123 7991 7971 6527 3169 3259 19 22465 0 0 0 45397 16473 15555 15289 11654 6759 5158 5849 14095 49964 0 46672 45397
46 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 68928 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 58944 0 0
47 7598 6834 7092 7321 7069 5339 1937 605 1719 5013 6778 56075 5779 3530 3729 4733 4821 2916 6 3 1 0 6778 121087 5131 2525 2759 3544 3446 2712 2181
3203 2754 8013 58119 0 5622 3495 2976 2458 2257 2909 4115 4601 0 0 0 0 7270 6644 5988 4635 3851 4297 5344 5208 0 0 128482 0
48 137431 95915 64912 51927 59703 85645 104042 112063 117735 124605 127786 142405 139048 64412 36311 26347 29928 50757 70154 78202 73213 64007 66657 109759 168762 23021 18433 48930 58631 58371 62392
69475 68680 53216 48956 99586 0 2 40164 83552 84052 63303 52597 55811 63152 65154 69579 111480 0 0 172793 137380 120467 91938 83260 90111 108895 127705 133539 146052
49 9728 9728 9728 18315 29561 26640 22450 17976 18094 22354 25949 29155 0 0 0 7711 22338 23238 17105 11680 9650 10749 13830 23221 0 0 22986 14120 14156 19901 14240
13467 14539 11773 10961 22226 128482 0 62601 41391 3 29 4425 14538 20545 18364 16648 26142 0 0 0 132205 4845 6896 7584 23772 32944 34660 32550 35295
50 6588 6588 6588 13176 36271 53114 41352 31916 27162 29234 33822 39538 3294 0 0 0 15738 44420 37152 24098 15702 13956 18238 32318 0 0 13176 36809 11500 21760 31010
23370 20346 16604 15808 32104 44310 103254 0 94535 38894 20 114 10528 24080 27364 25790 38916 129191 0 0 0 139436 4354 13674 17214 41090 51918 50590 53432
51 18502 21951 13364 9004 21258 52326 63029 46784 37981 35090 36959 44004 18502 7890 0 0 0 26740 58179 41886 25356 17298 19646 35615 17388 0 14872 24446 35017 8230 27212
35234 25361 17600 16806 34566 17388 15160 75540 0 95409 30093 1178 1317 14398 24637 27436 41103 71029 139616 0 0 0 121201 4245 19939 25441 47912 53098 55780
52 42771 50569 46626 24642 15217 29221 59017 65292 51544 45704 43419 49957 32950 26657 16426 0 0 0 33178 60236 39876 24288 21815 37953 28234 11377 7950 29286 28557 30845 8811
28758 31641 18588 15571 32798 27104 7439 31682 72374 0 85710 30559 2630 2975 13711 21820 35272 36573 31079 144500 0 0 0 117109 5342 22090 26520 40310 44718
53 59328 59737 73382 61451 32289 20186 33392 62275 71728 60474 54110 58384 40556 31800 41664 26278 0 0 0 32993 54547 35949 26485 41079 30807 16752 18096 14382 33863 29365 31430
12585 26308 22020 15348 31181 26154 10521 4418 42319 77440 0 80926 38907 3547 5118 14556 28739 24421 22133 14543 137189 0 0 0 126192 7935 20790 23218 31134
54 58384 54110 60474 71728 62275 33392 20186 32289 61451 73382 59737 59328 41079 26485 35949 54547 32993 0 0 0 26278 41664 31800 40556 31181 15348 22020 26308 12585 31430 29365
33863 14382 18096 16752 30807 28739 14556 5118 3547 38907 80926 0 77440 42319 4418 10521 26154 31134 23218 20790 7935 126192 0 0 0 137189 14543 22133 24421
55 49957 43419 45704 51544 65292 59017 29221 15217 24642 46626 50569 42771 37953 21815 24288 39876 60236 33178 0 0 0 16426 26657 32950 32798 15571 18588 31641 28758 8811 30845
28557 29286 7950 11377 28234 35272 21820 13711 2975 2630 30559 85710 0 72374 31682 7439 27104 44718 40310 26520 22090 5342 117109 0 0 0 144500 31079 36573
56 44004 36959 35090 37981 46784 63029 52326 21258 9004 13364 21951 18502 35615 19646 17298 25356 41886 58179 26740 0 0 0 7890 18502 34566 16806 17600 25361 35234 27212 8230
35017 24446 14872 0 17388 41103 27436 24637 14398 1317 1178 30093 95409 0 75540 15160 17388 55780 53098 47912 25441 19939 4245 121201 0 0 0 139616 71029
57 39538 33822 29234 27162 31916 41352 53114 36271 13176 6588 6588 6588 32318 18238 13956 15702 24098 37152 44420 15738 0 0 0 3294 32104 15808 16604 20346 23370 31010 21760
11500 36809 13176 0 0 38916 25790 27364 24080 10528 114 20 38894 94535 0 103254 44310 53432 50590 51918 41090 17214 13674 4354 139436 0 0 0 129191
58 29155 25949 22354 18094 17976 22450 26640 29561 18315 9728 9728 9728 23221 13830 10749 9650 11680 17105 23238 22338 7711 0 0 0 22226 10961 11773 14539 13467 14240 19901
14156 14120 22986 0 0 26142 16648 18364 20545 14538 4425 29 3 41391 62601 0 128482 35295 32550 34660 32944 23772 7584 6896 4845 132205 0 0 0
59 142405 127786 124605 117735 112063 104042 85645 59703 51927 64912 95915 137431 109759 66657 64007 73213 78202 70154 50757 29928 26347 36311 64412 139048 99586 48956 53216 68680 69475 62392 58371
58631 48930 18433 23021 168762 111480 69579 65154 63152 55811 52597 63303 84052 83552 40164 2 0 146052 133539 127705 108895 90111 83260 91938 120467 137380 172793 0 0
Sum of all rows = 4(3*0 + 1*2 + 1*18433 + 1*23021 + 1*26347 + 1*29928 + 1*36311 + 1*40164 + 1*48930 + 1*48956 + 1*50757 + 1*51927 + 1*52597 + 1*53216 + 1*55811 + 1*58371 + 1*58631 + 1*59703 + 1*62392 + 1*63152 +
1*63303 + 1*64007 + 1*64412 + 1*64912 + 1*65154 + 1*66657 + 1*68680 + 1*69475 + 1*69579 + 1*70154 + 1*73213 + 1*78202 + 1*83260 + 1*83552 + 1*84052 + 1*85645 + 1*90111 + 1*91938 + 1*95915 +
1*99586 + 1*104042 + 1*108895 + 1*109759 + 1*111480 + 1*112063 + 1*117735 + 1*120467 + 1*124605 + 1*127705 + 1*127786 + 1*133539 + 1*137380 + 1*137431 + 1*139048 + 1*142405 + 1*146052 +
1*168762 + 1*172793) +
4(9*0 + 1*3 + 1*29 + 1*4425 + 1*4845 + 1*6896 + 1*7584 + 1*7711 + 1*9650 + 3*9728 + 1*10749 + 1*10961 + 1*11680 + 1*11773 + 1*13467 + 1*13830 + 1*14120 + 1*14156 + 1*14240 + 1*14538 + 1*14539 +
1*16648 + 1*17105 + 1*17976 + 1*18094 + 1*18315 + 1*18364 + 1*19901 + 1*20545 + 1*22226 + 1*22338 + 1*22354 + 1*22450 + 1*22986 + 1*23221 + 1*23238 + 1*23772 + 1*25949 + 1*26142 + 1*26640 +
1*29155 + 1*29561 + 1*32550 + 1*32944 + 1*34660 + 1*35295 + 1*41391 + 1*62601 + 1*128482 + 1*132205) +
4(9*0 + 1*20 + 1*114 + 1*3294 + 1*4354 + 3*6588 + 1*10528 + 1*11500 + 2*13176 + 1*13674 + 1*13956 + 1*15702 + 1*15738 + 1*15808 + 1*16604 + 1*17214 + 1*18238 + 1*20346 + 1*21760 + 1*23370 +
1*24080 + 1*24098 + 1*25790 + 1*27162 + 1*27364 + 1*29234 + 1*31010 + 1*31916 + 1*32104 + 1*32318 + 1*33822 + 1*36271 + 1*36809 + 1*37152 + 1*38894 + 1*38916 + 1*39538 + 1*41090 + 1*41352 +
1*44310 + 1*44420 + 1*50590 + 1*51918 + 1*53114 + 1*53432 + 1*94535 + 1*103254 + 1*129191 + 1*139436) +
4(8*0 + 1*1178 + 1*1317 + 1*4245 + 1*7890 + 1*8230 + 1*9004 + 1*13364 + 1*14398 + 1*14872 + 1*15160 + 1*16806 + 1*17298 + 2*17388 + 1*17600 + 2*18502 + 1*19646 + 1*19939 + 1*21258 + 1*21951 +
1*24446 + 1*24637 + 1*25356 + 1*25361 + 1*25441 + 1*26740 + 1*27212 + 1*27436 + 1*30093 + 1*34566 + 1*35017 + 1*35090 + 1*35234 + 1*35615 + 1*36959 + 1*37981 + 1*41103 + 1*41886 + 1*44004 +
1*46784 + 1*47912 + 1*52326 + 1*53098 + 1*55780 + 1*58179 + 1*63029 + 1*71029 + 1*75540 + 1*95409 + 1*121201 + 1*139616) +
4(7*0 + 1*2630 + 1*2975 + 1*5342 + 1*7439 + 1*7950 + 1*8811 + 1*11377 + 1*13711 + 1*15217 + 1*15571 + 1*16426 + 1*18588 + 1*21815 + 1*21820 + 1*22090 + 1*24288 + 1*24642 + 1*26520 + 1*26657 +
1*27104 + 1*28234 + 1*28557 + 1*28758 + 1*29221 + 1*29286 + 1*30559 + 1*30845 + 1*31079 + 1*31641 + 1*31682 + 1*32798 + 1*32950 + 1*33178 + 1*35272 + 1*36573 + 1*37953 + 1*39876 + 1*40310 +
1*42771 + 1*43419 + 1*44718 + 1*45704 + 1*46626 + 1*49957 + 1*50569 + 1*51544 + 1*59017 + 1*60236 + 1*65292 + 1*72374 + 1*85710 + 1*117109 + 1*144500) +
4(7*0 + 1*3547 + 1*4418 + 1*5118 + 1*7935 + 1*10521 + 1*12585 + 1*14382 + 1*14543 + 1*14556 + 1*15348 + 1*16752 + 1*18096 + 1*20186 + 1*20790 + 1*22020 + 1*22133 + 1*23218 + 1*24421 + 1*26154 +
1*26278 + 1*26308 + 1*26485 + 1*28739 + 1*29365 + 1*30807 + 1*31134 + 1*31181 + 1*31430 + 1*31800 + 1*32289 + 1*32993 + 1*33392 + 1*33863 + 1*35949 + 1*38907 + 1*40556 + 1*41079 + 1*41664 +
1*42319 + 1*54110 + 1*54547 + 1*58384 + 1*59328 + 1*59737 + 1*60474 + 1*61451 + 1*62275 + 1*71728 + 1*73382 + 1*77440 + 1*80926 + 1*126192 + 1*137189) +
4(9*0 + 1*1 + 1*3 + 1*6 + 1*605 + 1*1719 + 1*1937 + 1*2181 + 1*2257 + 1*2458 + 1*2525 + 1*2712 + 1*2754 + 1*2759 + 1*2909 + 1*2916 + 1*2976 + 1*3203 + 1*3446 + 1*3495 + 1*3530 + 1*3544 +
1*3729 + 1*3851 + 1*4115 + 1*4297 + 1*4601 + 1*4635 + 1*4733 + 1*4821 + 1*5013 + 1*5131 + 1*5208 + 1*5339 + 1*5344 + 1*5622 + 1*5779 + 1*5988 + 1*6644 + 2*6778 + 1*6834 + 1*7069 + 1*7092 +
1*7270 + 1*7321 + 1*7598 + 1*8013 + 1*56075 + 1*58119 + 1*121087 + 1*128482) +
4(58*0 + 1*58944 + 1*68928) +
4(14*0 + 1*19 + 1*1481 + 1*3169 + 1*3259 + 1*4984 + 1*5003 + 1*5158 + 1*5378 + 1*5849 + 1*5914 + 1*6468 + 1*6527 + 1*6759 + 1*6873 + 1*7087 + 1*7496 + 1*7941 + 1*7971 + 1*7991 + 1*8183 +
1*8958 + 1*10166 + 1*10171 + 1*10256 + 1*10456 + 1*10657 + 1*11094 + 1*11466 + 1*11654 + 1*12123 + 1*12687 + 1*12944 + 1*14095 + 1*15136 + 1*15289 + 1*15555 + 1*16473 + 1*16828 + 1*17458 +
1*22465 + 1*23693 + 1*38844 + 2*45397 + 1*46672 + 1*49964) +
4(13*0 + 1*114 + 1*2350 + 1*4805 + 1*7162 + 1*7930 + 4*7981 + 1*9468 + 1*10604 + 1*11194 + 1*11738 + 1*12072 + 1*12124 + 1*12410 + 1*13088 + 1*14302 + 1*15294 + 1*15444 + 1*15786 + 1*17424 +
1*18297 + 1*19412 + 1*20658 + 1*20700 + 1*21128 + 1*21480 + 1*22086 + 1*23321 + 1*23324 + 1*23662 + 1*23842 + 1*27068 + 1*27326 + 1*27820 + 1*27900 + 1*29162 + 1*31514 + 1*33267 + 1*35342 +
1*39432 + 1*39786 + 1*41248 + 1*43945 + 1*47854 + 1*64606) +
4(13*0 + 1*381 + 1*2654 + 1*3359 + 1*7779 + 1*7796 + 1*7962 + 1*8877 + 1*9630 + 1*9882 + 1*10468 + 1*12437 + 1*12690 + 1*12938 + 1*13934 + 1*14764 + 1*14800 + 1*15394 + 1*15592 + 1*16054 +
1*16229 + 1*17399 + 1*17425 + 1*18246 + 1*19206 + 1*19336 + 1*21178 + 1*21301 + 1*21329 + 1*22649 + 1*22765 + 1*23004 + 1*25861 + 1*25862 + 1*25906 + 1*27002 + 1*29478 + 1*31672 + 1*32200 +
1*34490 + 1*35640 + 1*36172 + 1*37159 + 1*44656 + 1*48640 + 1*48720 + 1*53870 + 1*66718) +
4(13*0 + 1*1020 + 1*2710 + 1*3450 + 1*4160 + 1*7192 + 1*7896 + 1*8074 + 1*8272 + 1*9852 + 1*10600 + 1*11926 + 1*13240 + 1*13812 + 1*13830 + 1*14372 + 1*14580 + 1*14636 + 1*14826 + 1*15808 +
1*16364 + 1*16424 + 1*16501 + 1*16602 + 1*17584 + 1*17992 + 1*18296 + 1*18562 + 1*18908 + 1*21100 + 1*21472 + 1*21552 + 1*21780 + 1*23038 + 1*25052 + 1*26340 + 1*26808 + 1*30096 + 1*32408 +
1*35138 + 1*35980 + 1*36520 + 1*42978 + 1*43644 + 1*46020 + 1*48596 + 1*59118 + 1*62417) +
2(54*0 + 2*40279 + 2*109207 + 2*125793) +
2(50*0 + 2*8021 + 4*15006 + 2*23172 + 2*43328) +
2(5*0 + 2*7536 + 1*8736 + 2*10100 + 2*12232 + 1*15752 + 2*15930 + 1*17128 + 2*17390 + 1*17704 + 1*18344 + 2*19728 + 2*20836 + 1*21680 + 2*21920 + 1*21944 + 2*22060 + 2*22096 + 2*22112 +
2*28455 + 2*30566 + 2*31312 + 1*32024 + 2*33560 + 2*35576 + 2*36760 + 2*40320 + 2*40704 + 2*42052 + 2*46392 + 2*48966 + 2*49962 + 1*59604) +
2(5*0 + 1*12188 + 2*14691 + 2*14797 + 2*19055 + 2*21592 + 1*23458 + 1*25550 + 2*27204 + 2*27587 + 2*30284 + 1*30432 + 1*30472 + 2*31083 + 2*31541 + 2*32607 + 1*32650 + 2*33763 + 2*34207 +
1*34936 + 2*35515 + 1*37808 + 2*39652 + 2*41036 + 1*47662 + 2*48803 + 2*52813 + 2*52962 + 2*54868 + 2*56552 + 2*60602 + 2*62586 + 2*69079) +
2(5*0 + 1*12060 + 2*13916 + 1*13950 + 2*16005 + 2*17416 + 2*17505 + 2*22566 + 1*22780 + 1*24880 + 2*26400 + 2*27337 + 1*27360 + 2*27764 + 1*29424 + 2*31556 + 2*31608 + 2*31844 + 2*32388 +
2*33226 + 2*34604 + 1*35970 + 2*37506 + 2*40005 + 2*41715 + 1*42328 + 1*46012 + 2*51096 + 2*54915 + 2*59134 + 2*60546 + 2*61160 + 2*66726) +
2(5*0 + 1*11244 + 2*11798 + 2*12096 + 1*12244 + 2*13668 + 2*15812 + 1*18656 + 2*18910 + 2*19362 + 1*20492 + 1*20692 + 2*26254 + 2*26828 + 2*27920 + 2*28882 + 2*29134 + 2*30220 + 2*31810 +
2*32221 + 2*34968 + 2*35892 + 1*36332 + 1*38072 + 1*41336 + 2*42348 + 1*42420 + 2*45712 + 2*51328 + 2*55572 + 2*55796 + 2*57172 + 2*59890)
= 18849612 + 4725952 + 6645824 + 7160064 + 7557164 + 8001696 + 1122604 + 511488 + 2517632 + 3917652 + 4166016 + 4030184 + 1122604 + 1101116 + 418132 + 3052092 + 4121828 + 3857280 + 3537348
= 86416288
Value repetition frequencies = 4(57*1 + 1*3) +
4(48*1 + 1*3 + 1*9) +
4(46*1 + 1*2 + 1*3 + 1*9) +
4(48*1 + 2*2 + 1*8) +
4(53*1 + 1*7) +
4(53*1 + 1*7) +
4(49*1 + 1*2 + 1*9) +
4(2*1 + 1*58) +
4(44*1 + 1*2 + 1*14) +
4(43*1 + 1*4 + 1*13) +
4(47*1 + 1*13) +
4(47*1 + 1*13) +
2(3*2 + 1*54) +
2(3*2 + 1*4 + 1*50) +
2(9*1 + 23*2 + 1*5) +
2(9*1 + 23*2 + 1*5) +
2(9*1 + 23*2 + 1*5) +
2(9*1 + 23*2 + 1*5)
= 3600
Number of distinct row element sets = 19
Number of rows = 8*2 + 11*4
= 60
Number of distinct values = 676
Distinct values 0 1 2 3 6 19 20 29 114 381 605 1020 1178 1317 1481 1719 1937 2181 2257 2350
Frequency 900 4 4 8 4 4 4 4 8 4 4 4 4 4 4 4 4 4 4 4
Distinct values 2458 2525 2630 2654 2710 2712 2754 2759 2909 2916 2975 2976 3169 3203 3259 3294 3359 3446 3450 3495
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 3530 3544 3547 3729 3851 4115 4160 4245 4297 4354 4418 4425 4601 4635 4733 4805 4821 4845 4984 5003
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 5013 5118 5131 5158 5208 5339 5342 5344 5378 5622 5779 5849 5914 5988 6468 6527 6588 6644 6759 6778
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 12 4 4 8
Distinct values 6834 6873 6896 7069 7087 7092 7162 7192 7270 7321 7439 7496 7536 7584 7598 7711 7779 7796 7890 7896
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 7930 7935 7941 7950 7962 7971 7981 7991 8013 8021 8074 8183 8230 8272 8736 8811 8877 8958 9004 9468
Frequency 4 4 4 4 4 4 16 4 4 4 4 4 4 4 2 4 4 4 4 4
Distinct values 9630 9650 9728 9852 9882 10100 10166 10171 10256 10456 10468 10521 10528 10600 10604 10657 10749 10961 11094 11194
Frequency 4 4 12 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 11244 11377 11466 11500 11654 11680 11738 11773 11798 11926 12060 12072 12096 12123 12124 12188 12232 12244 12410 12437
Frequency 2 4 4 4 4 4 4 4 4 4 2 4 4 4 4 2 4 2 4 4
Distinct values 12585 12687 12690 12938 12944 13088 13176 13240 13364 13467 13668 13674 13711 13812 13830 13916 13934 13950 13956 14095
Frequency 4 4 4 4 4 4 8 4 4 4 4 4 4 4 8 4 4 2 4 4
Distinct values 14120 14156 14240 14302 14372 14382 14398 14538 14539 14543 14556 14580 14636 14691 14764 14797 14800 14826 14872 15006
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 8
Distinct values 15136 15160 15217 15289 15294 15348 15394 15444 15555 15571 15592 15702 15738 15752 15786 15808 15812 15930 16005 16054
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 2 4 8 4 4 4 4
Distinct values 16229 16364 16424 16426 16473 16501 16602 16604 16648 16752 16806 16828 17105 17128 17214 17298 17388 17390 17399 17416
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 2 4 4 8 4 4 4
Distinct values 17424 17425 17458 17505 17584 17600 17704 17976 17992 18094 18096 18238 18246 18296 18297 18315 18344 18364 18433 18502
Frequency 4 4 4 4 4 4 2 4 4 4 4 4 4 4 4 4 2 4 4 8
Distinct values 18562 18588 18656 18908 18910 19055 19206 19336 19362 19412 19646 19728 19901 19939 20186 20346 20492 20545 20658 20692
Frequency 4 4 2 4 4 4 4 4 4 4 4 4 4 4 4 4 2 4 4 2
Distinct values 20700 20790 20836 21100 21128 21178 21258 21301 21329 21472 21480 21552 21592 21680 21760 21780 21815 21820 21920 21944
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 2 4 4 4 4 4 2
Distinct values 21951 22020 22060 22086 22090 22096 22112 22133 22226 22338 22354 22450 22465 22566 22649 22765 22780 22986 23004 23021
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 2 4 4 4
Distinct values 23038 23172 23218 23221 23238 23321 23324 23370 23458 23662 23693 23772 23842 24080 24098 24288 24421 24446 24637 24642
Frequency 4 4 4 4 4 4 4 4 2 4 4 4 4 4 4 4 4 4 4 4
Distinct values 24880 25052 25356 25361 25441 25550 25790 25861 25862 25906 25949 26142 26154 26254 26278 26308 26340 26347 26400 26485
Frequency 2 4 4 4 4 2 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 26520 26640 26657 26740 26808 26828 27002 27068 27104 27162 27204 27212 27326 27337 27360 27364 27436 27587 27764 27820
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 4 2 4 4 4 4 4
Distinct values 27900 27920 28234 28455 28557 28739 28758 28882 29134 29155 29162 29221 29234 29286 29365 29424 29478 29561 29928 30093
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 2 4 4 4 4
Distinct values 30096 30220 30284 30432 30472 30559 30566 30807 30845 31010 31079 31083 31134 31181 31312 31430 31514 31541 31556 31608
Frequency 4 4 4 2 2 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 31641 31672 31682 31800 31810 31844 31916 32024 32104 32200 32221 32289 32318 32388 32408 32550 32607 32650 32798 32944
Frequency 4 4 4 4 4 4 4 2 4 4 4 4 4 4 4 4 4 2 4 4
Distinct values 32950 32993 33178 33226 33267 33392 33560 33763 33822 33863 34207 34490 34566 34604 34660 34936 34968 35017 35090 35138
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 2 4 4 4 4
Distinct values 35234 35272 35295 35342 35515 35576 35615 35640 35892 35949 35970 35980 36172 36271 36311 36332 36520 36573 36760 36809
Frequency 4 4 4 4 4 4 4 4 4 4 2 4 4 4 4 2 4 4 4 4
Distinct values 36959 37152 37159 37506 37808 37953 37981 38072 38844 38894 38907 38916 39432 39538 39652 39786 39876 40005 40164 40279
Frequency 4 4 4 4 2 4 4 2 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 40310 40320 40556 40704 41036 41079 41090 41103 41248 41336 41352 41391 41664 41715 41886 42052 42319 42328 42348 42420
Frequency 4 4 4 4 4 4 4 4 4 2 4 4 4 4 4 4 4 2 4 2
Distinct values 42771 42978 43328 43419 43644 43945 44004 44310 44420 44656 44718 45397 45704 45712 46012 46020 46392 46626 46672 46784
Frequency 4 4 4 4 4 4 4 4 4 4 4 8 4 4 2 4 4 4 4 4
Distinct values 47662 47854 47912 48596 48640 48720 48803 48930 48956 48966 49957 49962 49964 50569 50590 50757 51096 51328 51544 51918
Frequency 2 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 51927 52326 52597 52813 52962 53098 53114 53216 53432 53870 54110 54547 54868 54915 55572 55780 55796 55811 56075 56552
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 57172 58119 58179 58371 58384 58631 58944 59017 59118 59134 59328 59604 59703 59737 59890 60236 60474 60546 60602 61160
Frequency 4 4 4 4 4 4 4 4 4 4 4 2 4 4 4 4 4 4 4 4
Distinct values 61451 62275 62392 62417 62586 62601 63029 63152 63303 64007 64412 64606 64912 65154 65292 66657 66718 66726 68680 68928
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 69079 69475 69579 70154 71029 71728 72374 73213 73382 75540 77440 78202 80926 83260 83552 84052 85645 85710 90111 91938
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 94535 95409 95915 99586 103254 104042 108895 109207 109759 111480 112063 117109 117735 120467 121087 121201 124605 125793 126192 127705
Frequency 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Distinct values 127786 128482 129191 132205 133539 137189 137380 137431 139048 139436 139616 142405 144500 146052 168762 172793
Frequency 4 8 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Sum of distinct value frequencies = 36*2 + 625*4 + 11*8 + 2*12 + 1*16 + 1*900
= 3600
Number of SN-EN pairs for which the number of CNSAPs is greater than zero = 4*2 + 2*6 + 2*10 + 4*46 + 12*47 + 12*51 + 4*52 + 8*53 + 8*55 + 4*57
= 2700
Number of SN-EN pairs, with SN != EN, for which the number of CNSAPs equals zero = 840
Number of possible SN-EN pairs with SN != EN = 59*60
= 3540
