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