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.

0, 1, 24, 1760, 411861, 551247139, 2883245852086, 85948329517780776, 11001968794030973784902, 7462399462450938863305238264

Offset: 1

Author

Christopher Hunt Gribble, Jul 05 2013

Keywords

• nonn
• more

Examples

			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:
    o__o__o__o    o__o__o__o    o__o__o__o    o__o  o__o
    |        |    |        |    |        |    |  |  |  |
    o  o__o__o    o  o__o  o    o__o__o  o    o  o  o  o
    |  |          |  |  |  |          |  |    |  |  |  |
    o  o__o__o    o  o  o  o    o__o__o  o    o  o__o  o
    |        |    |  |  |  |    |        |    |        |
    o__o__o__o    o__o  o__o    o__o__o__o    o__o__o__o
		

Links

• Giovanni Resta, Simple C program for computing a(1)-a(4)
• Ed Wynn, Enumeration of nonisomorphic Hamiltonian cycles on square grid graphs, arXiv:1402.0545 [math.CO], 2014.

Crossrefs

Cf. A003763, A209077, A063524, A227005, A227301.

Formula

A063524 + A227005 + A227257 + A227301 = A209077.

1*A063524 + 2*A227005 + 4*A227257 + 8*A227301 = A003763.

a(n) = A237429(n) + A237430(n). - Ed Wynn, Feb 07 2014

Extensions

a(4) from Giovanni Resta, Jul 11 2013

a(5)-a(10) from Ed Wynn, Feb 05 2014