A374306 - OEIS

A374306

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

%I #12 Jul 29 2024 12:36:53

%S 47,2221,94006,3527224,123159829,4110628551,133093672039,

%T 4216993511767,131454310596858,4046054885054361,123275425298494683,

%U 3724935782123793466,111781579014020685006,3335061533295212856274,99013139230297294579692,2927094675162133314593603

%N Number of growing self-avoiding walks with displacement n on a half-infinite strip of height 7 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 {0,1,2,3,4,5,6}. The GSAW must start at the point (0,0). The displacement of a GSAW is the difference between the largest and smallext x-values that it reaches.

%H Jay Pantone, <a href="/A374306/a374306.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 Five of the a(1) = 47 walks are:

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

%e | | | |

%e * * * * * * * * * * * * * * *

%e | | | |

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

%e | | | | | | | |

%e * * * * * * * * * * * * * * *

%e | | | | | |

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

%e | | | | | | |

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

%e | | | | |

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

%Y Cf. A078528, A374305.

%K nonn

%O 1,1

%A _Jay Pantone_, Jul 23 2024