A374303 - OEIS

%I #11 Jul 26 2024 16:34:28

%S 2,2,9,10,40,58,206,342,1121,2024,6020,11469,31574,62660,164376,

%T 336835,853656,1795319,4434739,9511931,23042967,50154356,119696075,

%U 263380585,621470158,1378659503,3225317853,7199055796,16732951708,37523280788,86787492382

%N Number of growing self-avoiding walks of length n on a half-infinite strip of height 6 with a trapped endpoint.

%C 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}. The GSAW must start at the point (0,0). The length of a GSAW is the number of edges.

%H Jay Pantone, <a href="/A374303/a374303.txt">generating function</a>

%H 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 See Links section for generating function.

%e The a(5) = 2 walks are:

%e >   *  *  *        *  *  *

%e >

%e >   *  *  *        *  *  *

%e >

%e >   *  *  *        *  *  *

%e >

%e >   *--*  *        *  *  *

%e >   |  |

%e >   *  *  *        *--*--*

%e >      |           |     |

%e >   *--*  *        *  *--*

%Y Cf. A078528, A374301.

%K nonn

%O 5,1

%A _Jay Pantone_, Jul 22 2024