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.

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

Links

Table of n, a(n) for n=1..66.

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

Adjacent sequences: A336766 A336767 A336768 * A336770 A336771 A336772

Keyword

nonn,walk,tabl

Author

Scott R. Shannon, Aug 04 2020

Status

approved