A374304 Number of growing self-avoiding walks with displacement n on a half-infinite strip of height 6 with a trapped endpoint.

23, 629, 15134, 323031, 6428665, 122523673, 2267420832, 41081096139, 732520397439, 12900298930153, 224940605616826, 3890634712091201, 66843522591221500, 1141958198925483582, 19416047904038468727, 328765736871514344297, 5547125910154291613320

Offset

1,1

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 displacement of a GSAW is the difference between the largest and smallext x-values that it reaches.

Links

Table of n, a(n) for n=1..17.

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

Five of the a(1) = 23 walks are:
 *--*  *      *  *  *      *  *  *      *  *  *      *--*  *
 |  |                                                |  |
 *  *  *      *--*  *      *--*  *      *  *  *      *  *  *
 |  |         |  |         |  |                      |  |
 *  *  *      *  *  *      *  *  *      *  *  *      *  *  *
    |         |  |            |                      |  |
 *--*  *      *  *  *      *--*  *      *--*  *      *  *  *
 |               |         |            |  |         |  |
 *  *  *      *--*  *      *--*  *      *  *  *      *  *  *
 |            |               |            |            |
 *  *  *      *  *  *      *--*  *      *--*  *      *--*  *

Crossrefs

Cf. A078528, A374303.

Sequence in context: A142750 A202667 A129991 * A265681 A023295 A169596

Adjacent sequences: A374301 A374302 A374303 * A374305 A374306 A374307

Keyword

nonn

Author

Jay Pantone, Jul 22 2024

Status

approved