cp's OEIS Frontend

A374301 Number of growing self-avoiding walks of length n on a half-infinite strip of height 5 with a trapped endpoint.

%I A374301 #18 Jul 26 2024 15:19:10
%S A374301 2,3,8,13,32,69,161,361,845,1846,4241,9132,20791,44908,101361,220149,
%T A374301 493710,1076528,2401244,5248819,11659368,25531485,56546077,123976603,
%U A374301 274020536,601294678,1327099050,2913847433,6424359845,14111695015,31089757238,68312316581
%N A374301 Number of growing self-avoiding walks of length n on a half-infinite strip of height 5 with a trapped endpoint.
%C A374301 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.
%H A374301 Jay Pantone, <a href="/A374301/a374301.txt">generating function</a>
%H A374301 Jay Pantone, A. R. Klotz, and E. Sullivan, <a href="https://arxiv.org/abs/2407.18205">Exactly-solvable self-trapping lattice walks. II. Lattices of arbitrary height.</a>, arXiv:2407.18205 [math.CO], 2024.
%F A374301 See Links section for generating function.
%e A374301 The a(5) = 2 walks are:
%e A374301 >   *  *  *        *  *  *
%e A374301 >
%e A374301 >   *  *  *        *  *  *
%e A374301 >
%e A374301 >   *--*  *        *  *  *
%e A374301 >   |  |
%e A374301 >   *  *  *        *--*--*
%e A374301 >      |           |     |
%e A374301 >   *--*  *        *  *--*
%Y A374301 Cf. A078528, A374299.
%K A374301 nonn
%O A374301 5,1
%A A374301 _Jay Pantone_, Jul 22 2024