cp's OEIS Frontend

A227257 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.

%I A227257 #40 Jun 30 2023 10:26:53
%S A227257 0,1,24,1760,411861,551247139,2883245852086,85948329517780776,
%T A227257 11001968794030973784902,7462399462450938863305238264
%N A227257 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 A227257 Giovanni Resta, <a href="/A227257/a227257.c.txt">Simple C program for computing a(1)-a(4)</a>
%H A227257 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 A227257 A063524 + A227005 + A227257 + A227301 = A209077.
%F A227257 1*A063524 + 2*A227005 + 4*A227257 + 8*A227301 = A003763.
%F A227257 a(n) = A237429(n) + A237430(n). - _Ed Wynn_, Feb 07 2014
%e A227257 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 A227257     o__o__o__o    o__o__o__o    o__o__o__o    o__o  o__o
%e A227257     |        |    |        |    |        |    |  |  |  |
%e A227257     o  o__o__o    o  o__o  o    o__o__o  o    o  o  o  o
%e A227257     |  |          |  |  |  |          |  |    |  |  |  |
%e A227257     o  o__o__o    o  o  o  o    o__o__o  o    o  o__o  o
%e A227257     |        |    |  |  |  |    |        |    |        |
%e A227257     o__o__o__o    o__o  o__o    o__o__o__o    o__o__o__o
%Y A227257 Cf. A003763, A209077, A063524, A227005, A227301.
%K A227257 nonn,more
%O A227257 1,3
%A A227257 _Christopher Hunt Gribble_, Jul 05 2013
%E A227257 a(4) from _Giovanni Resta_, Jul 11 2013
%E A227257 a(5)-a(10) from _Ed Wynn_, Feb 05 2014