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.

0, 0, 121, 578937, 58407351059, 134528360800075421, 7015812452559988037073365, 8235314565328229497795808499821534, 216740797236120772990968348272561831275923059, 127557553423846099192878370706037904215158660401579043097

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, arXiv:1402.0545 [math.CO], 2014.

Formula

A063524 + A227005 + A227257 + A227301 = A209077.

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

Example

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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|              |    |  |  |  |  |  |    |              |
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         |  |       |  |  |  |  |  |          |  |
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|              |    |        |  |  |    |              |
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      |  |          |  |  |        |       |  |
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|              |    |  |  |  |  |  |    |              |
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.
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|        |  |  |       |  |             |  |  |        |
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|  |  |        |    |              |    |        |  |  |
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|  |  |  |  |  |    |              |    |  |  |  |  |  |
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      |  |          |  |  |  |  |  |
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|              |    |  |  |        |
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         |  |       |        |  |  |
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|              |    |  |  |  |  |  |
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Crossrefs

Cf. A003763, A209077, A063524, A227005, A227257.

Sequence in context: A135825 A221392 A337728 * A261364 A317956 A136094

Adjacent sequences: A227298 A227299 A227300 * A227302 A227303 A227304

Keyword

nonn,hard

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