A374303 -id:A374303 - cp's OEIS frontend

A374305 Number of growing self-avoiding walks of length n on a half-infinite strip of height 7 with a trapped endpoint.

2, 2, 8, 11, 34, 70, 180, 423, 1035, 2557, 6106, 15039, 35538, 85561, 201870, 478444, 1129498, 2654505, 6270807, 14679261, 34662653, 81011176, 191059001, 446245461, 1050699473, 2453328994, 5766594972, 13462400943, 31595520207, 73752506984, 172876421034

Offset: 5

Jay Pantone, Jul 22 2024

nonn

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 {0,1,2,3,4,5,6}. The GSAW must start at the point (0,0). The length of a GSAW is the number of edges.

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

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.

Cf. A078528, A374303.

See Links section for generating function.

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

Original entry on oeis.org

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

Offset: 1

Jay Pantone, Jul 22 2024

nonn

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.

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

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.

Cf. A078528, A374303.

See Links section for generating function.

cp's OEIS Frontend

A374305 Number of growing self-avoiding walks of length n on a half-infinite strip of height 7 with a trapped endpoint.

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