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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. 6
0, 1, 24, 1760, 411861, 551247139, 2883245852086, 85948329517780776, 11001968794030973784902, 7462399462450938863305238264 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..10.

Giovanni Resta, Simple C program for computing a(1)-a(4)

Ed Wynn, Enumeration of nonisomorphic Hamiltonian cycles on square grid graphs (2014), arXiv:1402.0545

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

EXAMPLE

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

CROSSREFS

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

Sequence in context: A054777 A301392 A084224 * A222999 A166788 A123794

Adjacent sequences:  A227254 A227255 A227256 * A227258 A227259 A227260

KEYWORD

nonn,more

AUTHOR

Christopher Hunt Gribble, Jul 05 2013

EXTENSIONS

a(4) from Giovanni Resta, Jul 11 2013

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

STATUS

approved

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Last modified July 30 17:21 EDT 2021. Contains 346359 sequences. (Running on oeis4.)