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%I #57 Jun 30 2023 10:26:45
%S 1,2,149,580717,58407763266,134528361351329451,
%T 7015812452562871283559623,8235314565328229583744138065519908,
%U 216740797236120772990979350241355889872437894,127557553423846099192878370713500303677609606263171680998
%N Number of Hamiltonian circuits (or self-avoiding rook's tours) on a 2n X 2n grid reduced for symmetry, i.e., where rotations and reflections are not counted as distinct.
%C _Christopher Hunt Gribble_ confirms a(3), and reports that there are 121 figures with group of order 1, 24 with group of order 2, and 4 with group of order 4. Then 121*(8/1) + 24*(8/2) + 4*(8/4) = 1072 = A003763(3), 121 + 24 + 4 = 149 = a(3). - _N. J. A. Sloane_, Feb 22 2013
%D Jon Wild, Posting to Sequence Fans Mailing List, Dec 10 2011.
%H Mathoverflow, <a href="https://mathoverflow.net/questions/306794/counting-hamiltonian-cycles-in-n-times-n-square-grid">Counting Hamiltonian cycles in n x n square grid</a>, question asked by Joseph O'Rourke, Jul 25 2018.
%H Jon Wild, <a href="/A209077/a209077.png">Illustration of a(3)</a>
%H Ed Wynn, <a href="http://arxiv.org/abs/1402.0545">Enumeration of nonisomorphic Hamiltonian cycles on square grid graphs</a>, arXiv:1402.0545 [math.CO], 3 Feb 2014.
%H <a href="/index/Gra#graphs">Index entries for sequences related to graphs, Hamiltonian</a>
%Y Cf. A003763, A120443, A140519, A140521.
%K nonn
%O 1,2
%A _N. J. A. Sloane_, Mar 04 2012
%E a(5)-a(10) from _Ed Wynn_, Feb 05 2014
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