cp's OEIS Frontend

A374297 Number of growing self-avoiding walks of length n on a half-infinite strip of height 3 with a trapped endpoint.

%I A374297 #33 Jul 26 2024 15:18:58
%S A374297 1,2,2,6,10,20,41,79,146,285,538,1039,1982,3812,7272,13961,26686,
%T A374297 51161,97865,187518,358835,687327,1315616,2519472,4823116,9235610,
%U A374297 17681264,33855310,64817361,124105590,237610012,454943624,871035486,1667726103,3193049603
%N A374297 Number of growing self-avoiding walks of length n on a half-infinite strip of height 3 with a trapped endpoint.
%C A374297 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}. The GSAW must start at the point (0,0). The length of a GSAW is the number of edges.
%H A374297 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.
%H A374297 <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,0,0,-1,2,-4,-3,-2,0,-4,-4).
%F A374297 G.f.: x^4*(1 + x - 2*x^2 - x^5 + x^6 - 2*x^8 - 5*x^9 - 5*x^10 - 2*x^11 - 2*x^12)/((1 + x^4)*(1 - 2*x^2)*(1 - x - 2*x^3 - x^4 - 2*x^5 - 2*x^6)).
%e A374297 The a(4) = 1 and a(5) = 2 walks are:
%e A374297   *--*  *    *--*  *    *  *  *
%e A374297      |       |  |
%e A374297   *--*  *    *  *  *    *--*--*
%e A374297   |             |       |     |
%e A374297   *     *    *--*  *    *  *--*
%e A374297 The GSAW below has length 10.
%e A374297   *--*--*  *  *  *
%e A374297         |
%e A374297   *--*  *--*  *  *
%e A374297   |  |     |
%e A374297   *  *--*--*  *  *
%Y A374297 Cf. A078528.
%K A374297 nonn,easy
%O A374297 4,2
%A A374297 _Jay Pantone_, Jul 03 2024