A374303 Number of growing self-avoiding walks of length n on a half-infinite strip of height 6 with a trapped endpoint.

2, 2, 9, 10, 40, 58, 206, 342, 1121, 2024, 6020, 11469, 31574, 62660, 164376, 336835, 853656, 1795319, 4434739, 9511931, 23042967, 50154356, 119696075, 263380585, 621470158, 1378659503, 3225317853, 7199055796, 16732951708, 37523280788, 86787492382

Offset

5,1

Comments

A growing self-avoiding walk (GSAW) is a walk on a graph that is directed, does not visit the same vertex twice, and for which all neighbors of the endpoint are part of the walk, i.e., the endpoint is trapped. This sequence is about GSAWs on the grid graph of integer points (x,y) where x >= 0 and y is in {0,1,2,3,4,5}. The GSAW must start at the point (0,0). The length of a GSAW is the number of edges.

Links

Table of n, a(n) for n=5..35.

Jay Pantone, generating function

Jay Pantone, Alexander R. Klotz, and Everett Sullivan, Exactly-solvable self-trapping lattice walks. II. Lattices of arbitrary height., arXiv:2407.18205 [math.CO], 2024.

Formula

See Links section for generating function.

Example

The a(5) = 2 walks are:
>   *  *  *        *  *  *
>
>   *  *  *        *  *  *
>
>   *  *  *        *  *  *
>
>   *--*  *        *  *  *
>   |  |
>   *  *  *        *--*--*
>      |           |     |
>   *--*  *        *  *--*

Crossrefs

Cf. A078528, A374301.

Sequence in context: A193726 A143022 A154100 * A372641 A002880 A225465

Adjacent sequences: A374300 A374301 A374302 * A374304 A374305 A374306

Keyword

nonn

Author

Jay Pantone, Jul 22 2024

Status

approved