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%I #19 Jan 30 2022 15:55:54
%S 1,256,117204,68939685,43598351250,28467653231928,18879702000329222,
%T 12620031290571348940,8469937551020819909757,
%U 5696439378813116535052879,3835239247888770485464962184,2583576672252172117218927779417,1740899369113326621618848563838108
%N Number of Hamiltonian paths in a 10 X (2n+1) grid starting at the lower left corner and finishing in the upper right corner.
%H Andrew Howroyd, <a href="/A333585/b333585.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Gra#graphs">Index entries for sequences related to graphs, Hamiltonian</a>
%o (Python)
%o # Using graphillion
%o from graphillion import GraphSet
%o import graphillion.tutorial as tl
%o def A333580(n, k):
%o if n == 1 or k == 1: return 1
%o universe = tl.grid(n - 1, k - 1)
%o GraphSet.set_universe(universe)
%o start, goal = 1, k * n
%o paths = GraphSet.paths(start, goal, is_hamilton=True)
%o return paths.len()
%o def A333585(n):
%o return A333580(10, 2 * n + 1)
%o print([A333585(n) for n in range(7)])
%Y Cf. A014523, A333580.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Mar 27 2020
%E Terms a(7) and beyond from _Andrew Howroyd_, Jan 30 2022
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