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%I #24 Jun 30 2023 10:20:21
%S 0,1,3,20,244,6891,378813,47917598,12118420172,6998287399637
%N Number of nonisomorphic Hamiltonian cycles on 2n X 2n square grid of points with exactly two axes of reflective symmetry.
%H Ed Wynn, <a href="https://arxiv.org/abs/1402.0545">Enumeration of nonisomorphic Hamiltonian cycles on square grid graphs</a>, arXiv:1402.0545 [math.CO], 2014.
%e Examples of 2 of the 3 classes for n=3. Note that all examples also have two-fold (but not four-fold) rotational symmetry.
%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, A227005, A237432.
%K nonn,walk,more
%O 1,3
%A _Ed Wynn_, Feb 07 2014