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A068393 Number of partitions of n X n checkerboard by two edgewise-connected sets which produce the maximum n^2-2n+2 frontier edges between the two sets. Partitions equal under rotation or reflection are counted only once. 3
2, 3, 7, 44, 494, 748827, 99987552, 23904291912, 23904291912, 14647978829979, 16186345621426754, 45843626565163628751, 235646717730827228414584, 3099290829556018890177304005 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

For even n > 2 the only symmetry possible is rotation by 180 degrees. For odd n > 1 the only symmetries are reflections either horizontally or vertically. - Andrew Howroyd, Apr 15 2016

LINKS

Table of n, a(n) for n=2..15.

EXAMPLE

From Andrew Howroyd, Apr 15 2016: (Start)

Case n=4: There are 2 nonisomorphic symmetrical solutions (see illustration below). a(4)=(A068381(4)/8 + 2)/2 = 7.

    __.__.__.__.    __.__.__.__.

   |   __    __|   |   __   |  |

   |  |  |  |  |   |  |  |  |  |

   |__|  |__|  |   |  |  |__|  |

   |__.__.__.__|   |__|__.__.__|

Case n=5: There are 7 nonisomorphic symmetrical solutions (see illustration below). a(5)=(A068381(5)/8 + 7)/2 = 44.

    __.__.__.__.__.   __.__.__.__.__.   __.__.__.__.__.   __.__.__.__.__.

   |   __|  |__   |  |   __|  |__   |  |  |__    __|  |  |  |   __   |  |

   |  |__    __|  |  |  |   __   |  |  |   __|  |__   |  |  |  |  |  |  |

   |   __|  |__   |  |  |  |  |  |  |  |  |   __   |  |  |  |  |  |  |  |

   |  |__.__.__|  |  |  |__|  |__|  |  |  |__|  |__|  |  |  |__|  |__|  |

   |__.__.__.__.__|  |__.__.__.__.__|  |__.__.__.__.__|  |__.__.__.__.__|

    __.__.__.__.__.   __.__.__.__.__.   __.__.__.__.__.

   |__.__    __.__|  |__    __    __|  |   __    __   |

   |   __|  |__   |  |  |  |  |  |  |  |__|  |  |  |__|

   |  |   __   |  |  |  |  |  |  |  |  |   __|  |__   |

   |  |__|  |__|  |  |  |__|  |__|  |  |  |__.__.__|  |

   |__.__.__.__.__|  |__.__.__.__.__|  |__.__.__.__.__|

(End)

CROSSREFS

Cf. A068381, A068416, A068392, A265914.

Sequence in context: A071580 A267507 A014546 * A032053 A086542 A058181

Adjacent sequences:  A068390 A068391 A068392 * A068394 A068395 A068396

KEYWORD

nonn

AUTHOR

R. H. Hardin, Mar 03 2002

EXTENSIONS

a(7)-a(15) from Andrew Howroyd, Apr 15 2016

STATUS

approved

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Last modified December 12 01:57 EST 2019. Contains 329948 sequences. (Running on oeis4.)