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%I #40 Jun 30 2023 10:26:53
%S 0,1,24,1760,411861,551247139,2883245852086,85948329517780776,
%T 11001968794030973784902,7462399462450938863305238264
%N Number of Hamiltonian circuits in a 2n X 2n square lattice of nodes, reduced for symmetry, where the orbits under the symmetry group of the square, D4, have 4 elements.
%H Giovanni Resta, <a href="/A227257/a227257.c.txt">Simple C program for computing a(1)-a(4)</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], 2014.
%F A063524 + A227005 + A227257 + A227301 = A209077.
%F 1*A063524 + 2*A227005 + 4*A227257 + 8*A227301 = A003763.
%F a(n) = A237429(n) + A237430(n). - _Ed Wynn_, Feb 07 2014
%e When n = 2, there is only 1 Hamiltonian circuit in a 4 X 4 square lattice, where the orbits under the symmetry group of the square have 4 elements. The 4 elements are:
%e o__o__o__o 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 o o o o
%e | | | | | | | | | | | |
%e o o__o__o 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 o__o__o__o
%Y Cf. A003763, A209077, A063524, A227005, A227301.
%K nonn,more
%O 1,3
%A _Christopher Hunt Gribble_, Jul 05 2013
%E a(4) from _Giovanni Resta_, Jul 11 2013
%E a(5)-a(10) from _Ed Wynn_, Feb 05 2014
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