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

%I A374305 #10 Jul 26 2024 21:21:12
%S A374305 2,2,8,11,34,70,180,423,1035,2557,6106,15039,35538,85561,201870,
%T A374305 478444,1129498,2654505,6270807,14679261,34662653,81011176,191059001,
%U A374305 446245461,1050699473,2453328994,5766594972,13462400943,31595520207,73752506984,172876421034
%N A374305 Number of growing self-avoiding walks of length n on a half-infinite strip of height 7 with a trapped endpoint.
%C A374305 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.
%H A374305 Jay Pantone, <a href="/A374305/a374305.txt">generating function</a>
%H A374305 Jay Pantone, Alexander R. Klotz, and Everett 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 A374305 See Links section for generating function.
%e A374305 The a(5) = 2 walks are:
%e A374305 >   *  *  *        *  *  *
%e A374305 >
%e A374305 >   *  *  *        *  *  *
%e A374305 >
%e A374305 >   *  *  *        *  *  *
%e A374305 >
%e A374305 >   *  *  *        *  *  *
%e A374305 >
%e A374305 >   *--*  *        *  *  *
%e A374305 >   |  |
%e A374305 >   *  *  *        *--*--*
%e A374305 >      |           |     |
%e A374305 >   *--*  *        *  *--*
%Y A374305 Cf. A078528, A374303.
%K A374305 nonn
%O A374305 5,1
%A A374305 _Jay Pantone_, Jul 22 2024