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A374301
Number of growing self-avoiding walks of length n on a half-infinite strip of height 5 with a trapped endpoint.
3
2, 3, 8, 13, 32, 69, 161, 361, 845, 1846, 4241, 9132, 20791, 44908, 101361, 220149, 493710, 1076528, 2401244, 5248819, 11659368, 25531485, 56546077, 123976603, 274020536, 601294678, 1327099050, 2913847433, 6424359845, 14111695015, 31089757238, 68312316581
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}. The GSAW must start at the point (0,0). The length of a GSAW is the number of edges.
LINKS
Jay Pantone, generating function
Jay Pantone, A. R. Klotz, and E. 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
Sequence in context: A191393 A025082 A317911 * A151889 A366020 A294151
KEYWORD
nonn
AUTHOR
Jay Pantone, Jul 22 2024
STATUS
approved