A[i,0] = B[i,0] = 1.
A[i,j] = if 5*j < 2*i + 2 then A[i-1,j] + A[i,j-1] , else 0.
\i 1 2 3 4 5 6 7 8 9 10 11 12 13 14
j --------------------------------------------------------
0| 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1| 0 1 2 3 4 5 6 7 8 9 10 11 12 13
2| 0 0 0 0 4 9 15 22 30 39 49 60 72 85
3| 0 0 0 0 0 0 15 37 67 106 155 215 287 372
4| 0 0 0 0 0 0 0 0 0 106 261 476 763 1135
5| 0 0 0 0 0 0 0 0 0 0 0 476 1239 2374
.
B[i,j] = if 5*j < 2*i + 1 then B[i-1,j] + B[i,j-1], else 0.
\i 1 2 3 4 5 6 7 8 9 10 11 12 13 14
j --------------------------------------------------------
0| 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1| 0 0 1 2 3 4 5 6 7 8 9 10 11 12
2| 0 0 0 0 3 7 12 18 25 33 42 52 63 75
3| 0 0 0 0 0 0 0 18 43 76 118 170 233 308
4| 0 0 0 0 0 0 0 0 0 76 194 364 597 905
5| 0 0 0 0 0 0 0 0 0 0 0 0 597 1502
.
A+B:
\i 1 2 3 4 5 6 7 8 9 10 11 12 13 14
j --------------------------------------------------------
0| 2 2 2 2 2 2 2 2 2 2 2 2 2 2
1| 0 1 3 5 7 9 11 13 15 17 19 21 23 25
2| 0 0 0 0 7 16 27 40 55 72 91 112 135 160
3| 0 0 0 0 0 0 15 55 110 182 273 385 520 680
4| 0 0 0 0 0 0 0 0 0 182 455 840 1360 2040
5| 0 0 0 0 0 0 0 0 0 0 0 476 1836 3876
.
t = 1: a(1) = 5 because
A[5*1-1,2*1-1] = A[4,1] = 3, B[4,1] = 2, A[4,1]+B[4,1] = 5;
t = 2: a(2) = 110 because
A[5*2-1,2*2-1] = A[9,3] = 67, B[9,3] = 43, A[9,3]+B[9,3] = 110;
t = 3: a(3) = 3876 because
A[5*3-1,2*3-1] = A[14,5] = 2374, B[14,5] = 1502, A[14,5]+B[14,5] = 3876.
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