cp's OEIS Frontend

A374299 Number of growing self-avoiding walks of length n on a half-infinite strip of height 4 with a trapped endpoint.

%I A374299 #13 Jul 26 2024 13:38:56
%S A374299 3,2,9,8,36,45,153,235,658,1095,2760,4994,11757,22415,50587,99631,
%T A374299 218605,439382,947346,1929565,4113065,8450088,17879748,36937722,
%U A374299 77783590
%N A374299 Number of growing self-avoiding walks of length n on a half-infinite strip of height 4 with a trapped endpoint.
%C A374299 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}. The GSAW must start at the point (0,0). The length of a GSAW is the number of edges.
%H A374299 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 A374299 G.f.: ((12*x^39 + 14*x^38 - 20*x^37 - 18*x^36 - 45*x^35 - 12*x^34 + 107*x^33 - 38*x^32 + 3*x^31 - 49*x^30 - 38*x^29 + 242*x^28 - 11*x^27 - 66*x^26 - 181*x^25 - 144*x^24 + 246*x^23 + 91*x^22 + 72*x^21 - 208*x^20 - 150*x^19 + 98*x^18 + 57*x^17 + 143*x^16 - 74*x^15 + 5*x^14 - 21*x^13 + 28*x^12 - 17*x^11 - 55*x^10 - 17*x^9 + 22*x^8 + 45*x^7 + 10*x^6 - 19*x^5 - 21*x^4 + 3*x^3 + 7*x^2 + 4*x - 3)*x^5)/((2*x^19 + 2*x^18 - 7*x^17 - 6*x^16 + 5*x^15 + 8*x^14 + 7*x^13 - 17*x^12 - 8*x^11 + 3*x^10 + 10*x^9 + 3*x^8 - 8*x^7 + 2*x^6 - x^5 + 6*x^4 - 3*x^3 - 2*x + 1)*(4*x^20 - 2*x^18 - 5*x^16 + 8*x^14 - x^12 + 2*x^10 - 4*x^8 + 2*x^6 + 3*x^4 - 4*x^2 + 1)).
%e A374299 The a(5) = 3 walks are:
%e A374299   *--*  *        *  *  *        *  *  *
%e A374299      |
%e A374299   *--*  *        *--*  *        *  *  *
%e A374299   |              |  |
%e A374299   *  *  *        *  *  *        *--*--*
%e A374299   |                 |           |     |
%e A374299   *  *  *        *--*  *        *  *--*
%Y A374299 Cf. A078528.
%K A374299 nonn,easy
%O A374299 5,1
%A A374299 _Jay Pantone_, Jul 15 2024