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A333583 Number of Hamiltonian paths in an 8 X (2n+1) grid starting at the lower left corner and finishing in the upper right corner.

%I A333583 #15 Jan 30 2022 15:55:59
%S A333583 1,64,6706,851073,114243216,15695570146,2178079125340,303568139329711,
%T A333583 42388918310108440,5923750747499881068,828111786035239457647,
%U A333583 115782566867663040724929,16189114623816733581826838,2263672174616450290622937801,316525123224847580237219904819
%N A333583 Number of Hamiltonian paths in an 8 X (2n+1) grid starting at the lower left corner and finishing in the upper right corner.
%H A333583 Andrew Howroyd, <a href="/A333583/b333583.txt">Table of n, a(n) for n = 0..200</a>
%H A333583 <a href="/index/Gra#graphs">Index entries for sequences related to graphs, Hamiltonian</a>
%o A333583 (Python)
%o A333583 # Using graphillion
%o A333583 from graphillion import GraphSet
%o A333583 import graphillion.tutorial as tl
%o A333583 def A333580(n, k):
%o A333583     if n == 1 or k == 1: return 1
%o A333583     universe = tl.grid(n - 1, k - 1)
%o A333583     GraphSet.set_universe(universe)
%o A333583     start, goal = 1, k * n
%o A333583     paths = GraphSet.paths(start, goal, is_hamilton=True)
%o A333583     return paths.len()
%o A333583 def A333583(n):
%o A333583     return A333580(8, 2 * n + 1)
%o A333583 print([A333583(n) for n in range(7)])
%Y A333583 Cf. A014523, A333580.
%K A333583 nonn
%O A333583 0,2
%A A333583 _Seiichi Manyama_, Mar 27 2020
%E A333583 Terms a(7) and beyond from _Andrew Howroyd_, Jan 30 2022