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A374306 Number of growing self-avoiding walks with displacement n on a half-infinite strip of height 7 with a trapped endpoint.

%I A374306 #12 Jul 29 2024 12:36:53
%S A374306 47,2221,94006,3527224,123159829,4110628551,133093672039,
%T A374306 4216993511767,131454310596858,4046054885054361,123275425298494683,
%U A374306 3724935782123793466,111781579014020685006,3335061533295212856274,99013139230297294579692,2927094675162133314593603
%N A374306 Number of growing self-avoiding walks with displacement n on a half-infinite strip of height 7 with a trapped endpoint.
%C A374306 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 A374306 Jay Pantone, <a href="/A374306/a374306.txt">Generating function</a>.
%H A374306 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 A374306 See Links section for generating function.
%e A374306 Five of the a(1) = 47 walks are:
%e A374306  *--*  *      *  *  *      *  *  *      *  *  *      *--*  *
%e A374306  |  |                                                |  |
%e A374306  *  *  *      *  *  *      *  *  *      *  *  *      *  *  *
%e A374306  |  |                                                |  |
%e A374306  *  *  *      *--*  *      *--*  *      *  *  *      *  *  *
%e A374306  |  |         |  |         |  |                      |  |
%e A374306  *  *  *      *  *  *      *  *  *      *  *  *      *  *  *
%e A374306     |         |  |            |                      |  |
%e A374306  *--*  *      *  *  *      *--*  *      *--*  *      *  *  *
%e A374306  |               |         |            |  |         |  |
%e A374306  *  *  *      *--*  *      *--*  *      *  *  *      *  *  *
%e A374306  |            |               |            |            |
%e A374306  *  *  *      *  *  *      *--*  *      *--*  *      *--*  *
%Y A374306 Cf. A078528, A374305.
%K A374306 nonn
%O A374306 1,1
%A A374306 _Jay Pantone_, Jul 23 2024