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A333584 Number of Hamiltonian paths in a 9 X n grid starting at the lower left corner and finishing in the upper right corner.

%I A333584 #13 Mar 28 2020 05:20:27
%S A333584 1,1,128,624,28417,286395,8261289,114243216,2688307514,43598351250,
%T A333584 928370853748,16331387665387,330593938169845,6062963019120077,
%U A333584 119575303856316650,2240422461856052342,43592076562463162280,825830699757513748579,15955080499901505066753
%N A333584 Number of Hamiltonian paths in a 9 X n grid starting at the lower left corner and finishing in the upper right corner.
%H A333584 Seiichi Manyama, <a href="/A333584/b333584.txt">Table of n, a(n) for n = 1..200</a>
%H A333584 <a href="/index/Gra#graphs">Index entries for sequences related to graphs, Hamiltonian</a>
%o A333584 (Python)
%o A333584 # Using graphillion
%o A333584 from graphillion import GraphSet
%o A333584 import graphillion.tutorial as tl
%o A333584 def A333580(n, k):
%o A333584     if n == 1 or k == 1: return 1
%o A333584     universe = tl.grid(n - 1, k - 1)
%o A333584     GraphSet.set_universe(universe)
%o A333584     start, goal = 1, k * n
%o A333584     paths = GraphSet.paths(start, goal, is_hamilton=True)
%o A333584     return paths.len()
%o A333584 def A333584(n):
%o A333584     return A333580(n, 9)
%o A333584 print([A333584(n) for n in range(1, 20)])
%Y A333584 Row n=9 of A333580.
%Y A333584 Cf. A014584.
%K A333584 nonn
%O A333584 1,3
%A A333584 _Seiichi Manyama_, Mar 27 2020