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A227301 Number of Hamiltonian circuits in a 2n node X 2n node square lattice, reduced for symmetry, where the orbits under the symmetry group of the square, D4, have 8 elements.

%I A227301 #37 Jun 30 2023 10:26:58
%S A227301 0,0,121,578937,58407351059,134528360800075421,
%T A227301 7015812452559988037073365,8235314565328229497795808499821534,
%U A227301 216740797236120772990968348272561831275923059,127557553423846099192878370706037904215158660401579043097
%N A227301 Number of Hamiltonian circuits in a 2n node X 2n node square lattice, reduced for symmetry, where the orbits under the symmetry group of the square, D4, have 8 elements.
%H A227301 Giovanni Resta, <a href="/A227301/a227301.c.txt">Simple C program for computing a(1)-a(4)</a>
%H A227301 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 A227301 A063524 + A227005 + A227257 + A227301 = A209077.
%F A227301 1*A063524 + 2*A227005 + 4*A227257 + 8*A227301 = A003763.
%e A227301 When n = 3 there are 121 Hamiltonian circuits in a 6 X 6  square lattice where the orbits under the symmetry group of the square have 8 elements.  One of these circuits is shown below with its 8 distinct transformations under rotation and reflection:
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%Y A227301 Cf. A003763, A209077, A063524, A227005, A227257.
%K A227301 nonn,hard
%O A227301 1,3
%A A227301 _Christopher Hunt Gribble_, Jul 05 2013
%E A227301 a(4) from _Giovanni Resta_, Jul 11 2013
%E A227301 a(5)-a(10) from _Ed Wynn_, Feb 05 2014