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A336769
Table read by antidiagonals: T(h,n) is the number of n-step self avoiding walks on a 2D square grid confined to an infinite strip of height h where the walk starts at the origin.
1
3, 6, 3, 12, 7, 3, 20, 18, 7, 3, 36, 40, 19, 7, 3, 58, 86, 48, 19, 7, 3, 100, 170, 120, 49, 19, 7, 3, 160, 350, 274, 130, 49, 19, 7, 3, 268, 688, 620, 326, 131, 49, 19, 7, 3, 430, 1394, 1346, 810, 338, 131, 49, 19, 7, 3, 708, 2702, 2972, 1912, 884, 339, 131, 49, 19, 7, 3
OFFSET
1,1
FORMULA
For n <= h, T(h,n) = A116903(n).
Row 1 = T(1,n) = A038577(n).
Row 2 = T(2,n) = A302408(n).
EXAMPLE
T(1,3) = 12. The six 3-step walks taking a first step to the right or a first step upward followed by a step to the right are:
.
+ +--+ +--+ +--+--+ +--+
| | | | | |
+--+--+--+ +--+--+ +--+ +--+ + + +
.
The same steps can be taken to the left, giving a total of 2*6 = 12 walks.
.
The table begins:
.
3 6 12 20 36 58 100 160 268 430 708 1140 1860 3002 4876 7880...
3 7 18 40 86 170 350 688 1394 2702 5338 10278 20078 38578 74820 143496...
3 7 19 48 120 274 620 1346 2972 6402 13994 29870 64412 136308 291008 612920...
3 7 19 49 130 326 810 1912 4486 10262 23634 53642 122624 276524 627248 1405154...
3 7 19 49 131 338 884 2228 5560 13438 32320 76440 181202 425138 1001128 2336886...
3 7 19 49 131 339 898 2328 6050 15320 38478 94642 231798 560794 1357098 3258148...
3 7 19 49 131 339 899 2344 6180 16040 41572 105806 267560 666682 1655140 4070280...
3 7 19 49 131 339 899 2345 6198 16204 42586 110636 286682 733032 1865008 4693178...
3 7 19 49 131 339 899 2345 6199 16224 42788 112016 293908 764248 1982070 5089002...
3 7 19 49 131 339 899 2345 6199 16225 42810 112260 295734 774682 2030988 5286652...
3 7 19 49 131 339 899 2345 6199 16225 42811 112284 296024 777042 2045610 5360672...
3 7 19 49 131 339 899 2345 6199 16225 42811 112285 296050 777382 2048600 5380646...
3 7 19 49 131 339 899 2345 6199 16225 42811 112285 296051 777410 2048994 5384370...
3 7 19 49 131 339 899 2345 6199 16225 42811 112285 296051 777411 2049024 5384822...
3 7 19 49 131 339 899 2345 6199 16225 42811 112285 296051 777411 2049025 5384854...
3 7 19 49 131 339 899 2345 6199 16225 42811 112285 296051 777411 2049025 5384855...
...
CROSSREFS
Cf. A116903 (h->infinity), A038577 (h=1), A302408 (h=2), A001411, A038373.
Sequence in context: A275535 A160899 A360981 * A337035 A203491 A085709
KEYWORD
nonn,walk,tabl
AUTHOR
Scott R. Shannon, Aug 04 2020
STATUS
approved