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%I #19 Jun 30 2023 10:27:02
%S 0,1,19,1394,281990,377205809,1539951848735,44222409563201991,
%T 3842818845468254120853,2396657968905952750257244144
%N Number of nonisomorphic Hamiltonian cycles on 2n X 2n square grid of points with exactly one axis of reflective symmetry.
%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], 2014.
%F a(n) = A227257(n) - A237430(n).
%e The following two cycles with n=3 are counted only once, since they are isomorphic under the full symmetry group of the square. They have a horizontal and a vertical axis respectively. No example has a diagonal axis, since this brings other symmetries (see A063524).
%e o-o-o-o-o-o o-o o-o o-o
%e | | | | | | | |
%e o o-o-o-o-o o o o o o o
%e | | | | | | | |
%e o o-o-o-o-o o o o o o o
%e | | | | | | | |
%e o o-o-o-o-o o o o o o o
%e | | | | | | | |
%e o o-o-o o-o o o-o o-o o
%e | | | |
%e o-o-o-o-o-o o-o-o-o-o-o
%Y Cf. A209077, A227257, A237430.
%K nonn,walk,more
%O 1,3
%A _Ed Wynn_, Feb 07 2014