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A333581 Number of Hamiltonian paths in a 6 X (2n+1) grid starting at the lower left corner and finishing in the upper right corner.

%I A333581 #15 Jan 30 2022 15:56:04
%S A333581 1,16,378,10204,286395,8142184,232408228,6641558434,189856823709,
%T A333581 5427696641303,155171211771501,4436158800822989,126824318787312712,
%U A333581 3625748174071085779,103655548766966797516,2963380335725281547187,84719269552230266413889,2422015949371169505273833
%N A333581 Number of Hamiltonian paths in a 6 X (2n+1) grid starting at the lower left corner and finishing in the upper right corner.
%H A333581 Andrew Howroyd, <a href="/A333581/b333581.txt">Table of n, a(n) for n = 0..500</a>
%H A333581 <a href="/index/Gra#graphs">Index entries for sequences related to graphs, Hamiltonian</a>
%o A333581 (Python)
%o A333581 # Using graphillion
%o A333581 from graphillion import GraphSet
%o A333581 import graphillion.tutorial as tl
%o A333581 def A333580(n, k):
%o A333581     if n == 1 or k == 1: return 1
%o A333581     universe = tl.grid(n - 1, k - 1)
%o A333581     GraphSet.set_universe(universe)
%o A333581     start, goal = 1, k * n
%o A333581     paths = GraphSet.paths(start, goal, is_hamilton=True)
%o A333581     return paths.len()
%o A333581 def A333581(n):
%o A333581     return A333580(6, 2 * n + 1)
%o A333581 print([A333581(n) for n in range(10)])
%Y A333581 Cf. A014523, A333580.
%K A333581 nonn
%O A333581 0,2
%A A333581 _Seiichi Manyama_, Mar 27 2020
%E A333581 Terms a(10) and beyond from _Andrew Howroyd_, Jan 30 2022