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A333585 Number of Hamiltonian paths in a 10 X (2n+1) grid starting at the lower left corner and finishing in the upper right corner.

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