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A333582 Number of Hamiltonian paths in a 7 X n grid starting at the lower left corner and finishing in the upper right corner.

%I A333582 #17 Mar 28 2020 04:44:46
%S A333582 1,1,32,111,1670,10204,111712,851073,8261289,68939685,637113287,
%T A333582 5521505724,49977297839,440051896440,3947537767621,34992551369200,
%U A333582 312684850861298,2779712414621925,24796726969942763,220708765035288988,1967401456946216789,17520501580778152908
%N A333582 Number of Hamiltonian paths in a 7 X n grid starting at the lower left corner and finishing in the upper right corner.
%H A333582 Seiichi Manyama, <a href="/A333582/b333582.txt">Table of n, a(n) for n = 1..500</a>
%H A333582 <a href="/index/Gra#graphs">Index entries for sequences related to graphs, Hamiltonian</a>
%o A333582 (Python)
%o A333582 # Using graphillion
%o A333582 from graphillion import GraphSet
%o A333582 import graphillion.tutorial as tl
%o A333582 def A333580(n, k):
%o A333582     if n == 1 or k == 1: return 1
%o A333582     universe = tl.grid(n - 1, k - 1)
%o A333582     GraphSet.set_universe(universe)
%o A333582     start, goal = 1, k * n
%o A333582     paths = GraphSet.paths(start, goal, is_hamilton=True)
%o A333582     return paths.len()
%o A333582 def A333582(n):
%o A333582     return A333580(n, 7)
%o A333582 print([A333582(n) for n in range(1, 25)])
%Y A333582 Row n=7 of A333580.
%Y A333582 Cf. A014584.
%K A333582 nonn
%O A333582 1,3
%A A333582 _Seiichi Manyama_, Mar 27 2020