cp's OEIS Frontend

A227005 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 2 elements.

%I A227005 #48 Jun 30 2023 10:26:42
%S A227005 0,1,4,20,346,6891,634172,47917598,27622729933,6998287399637
%N A227005 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 2 elements.
%H A227005 Giovanni Resta, <a href="/A227005/a227005.c.txt">Simple C program for computing a(1)-a(4)</a>
%H A227005 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 A227005 A063524 + A227005 + A227257 + A227301 = A209077.
%F A227005 1*A063524 + 2*A227005 + 4*A227257 + 8*A227301 = A003763.
%F A227005 a(2n) = A237431(2n), a(2n+1) = A237431(2n+1) + A237432(n+1). -  _Ed Wynn_, Feb 07 2014
%e A227005 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 2 elements.  The 2 elements are:
%e A227005             o__o__o__o        o__o  o__o
%e A227005             |        |        |  |  |  |
%e A227005             o__o  o__o        o  o__o  o
%e A227005                |  |           |        |
%e A227005             o__o  o__o        o  o__o  o
%e A227005             |        |        |  |  |  |
%e A227005             o__o__o__o        o__o  o__o
%Y A227005 Cf. A003763, A209077, A063524, A227257, A227301.
%K A227005 nonn,more
%O A227005 1,3
%A A227005 _Christopher Hunt Gribble_, Jul 05 2013
%E A227005 a(4) from _Giovanni Resta_, Jul 11 2013
%E A227005 a(5)-a(10) from _Ed Wynn_, Feb 05 2014