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A319096 Number of nonequivalent ways to place n^2 nonattacking kings on a 2n X 2n chessboard under all symmetry operations of the square. 2
1, 14, 459, 35312, 4072108, 638653285, 128441726634, 31872148398195, 9490641145219266, 3321018871480028710 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A maximum of n^2 nonattacking kings may be placed on a 2n X 2n chessboard.

LINKS

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

FORMULA

a(n) = A236679(2n+1, n^2).

EXAMPLE

For n = 2 there are a(2) = 14 distinct solutions from 79 that will not be repeated at all possible turns and reflections.

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3.                  4.

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5.                  6.

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7.                  8.

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9.                  10.

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|   |   |   |   |   |   |   |   | * |

| * |   |   | * |   |   | * |   |   |

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11.                 12.

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| * |   | * |   |   | * |   |   | * |

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|   |   |   |   |   |   | * |   |   |

|   | * |   | * |   |   |   |   | * |

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13.                 14.

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| * |   |   | * |   |   | * |   |   |

|   |   |   |   |   |   |   |   | * |

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| * |   |   | * |   |   |   | * |   |

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CROSSREFS

Cf. A018807 (rotations and reflections considered distinct).

Cf. A137432 (on cylindrical chessboard).

Cf. A236679, A322284, A321614.

Sequence in context: A201546 A305115 A282245 * A297548 A215787 A005790

Adjacent sequences:  A319093 A319094 A319095 * A319097 A319098 A319099

KEYWORD

nonn,more

AUTHOR

Anton Nikonov, Dec 21 2018

EXTENSIONS

a(4)-a(10) from Andrew Howroyd, Dec 21 2018

STATUS

approved

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Last modified November 29 18:41 EST 2021. Contains 349416 sequences. (Running on oeis4.)