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A237429 Number of nonisomorphic Hamiltonian cycles on 2n X 2n square grid of points with exactly one axis of reflective symmetry. 2
0, 1, 19, 1394, 281990, 377205809, 1539951848735, 44222409563201991, 3842818845468254120853, 2396657968905952750257244144 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

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

Ed Wynn, Enumeration of nonisomorphic Hamiltonian cycles on square grid graphs, arXiv:1402.0545 [math.CO], 2014

FORMULA

a(n) = A227257(n) - A237430(n).

EXAMPLE

The following two cycles with n=3 are counted only once, since they are isomorphic under the full symmetry group of the square. They have a horizontal and a vertical axis respectively.  No example has a diagonal axis, since this brings other symmetries (see A063524).

  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-o-o   o-o-o-o-o-o

CROSSREFS

Cf. A209077, A227257, A237430.

Sequence in context: A107673 A130037 A047910 * A177611 A051847 A217830

Adjacent sequences:  A237426 A237427 A237428 * A237430 A237431 A237432

KEYWORD

nonn,walk

AUTHOR

Ed Wynn, Feb 07 2014

STATUS

approved

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Last modified November 14 03:52 EST 2018. Contains 317159 sequences. (Running on oeis4.)