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a(n) gives the number of configurations of non-attacking rooks up to symmetry on an n X n chessboard such that the number of distinct directions between the rooks is given by A321531(n).
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%I #9 Dec 14 2018 19:50:02

%S 1,1,1,1,2,21,11,74,89,18

%N a(n) gives the number of configurations of non-attacking rooks up to symmetry on an n X n chessboard such that the number of distinct directions between the rooks is given by A321531(n).

%C Conjecture: a(n) = A321532(n)/8 for n >= 4.

%e For n = 5, the a(5) = 2 essentially different configurations of nonattacking rooks with the maximal number of directions between them are given by the following two chessboards:

%e +---+---+---+---+---+

%e 5| X | | | | |

%e +---+---+---+---+---+

%e 4| | | X | | |

%e +---+---+---+---+---+

%e 3| | | | X | |

%e +---+---+---+---+---+

%e 2| | | | | X |

%e +---+---+---+---+---+

%e 1| | X | | | |

%e +---+---+---+---+---+

%e A B C D E

%e +---+---+---+---+---+

%e 5| X | | | | |

%e +---+---+---+---+---+

%e 4| | | | X | |

%e +---+---+---+---+---+

%e 3| | | X | | |

%e +---+---+---+---+---+

%e 2| | | | | X |

%e +---+---+---+---+---+

%e 1| | X | | | |

%e +---+---+---+---+---+

%e A B C D E

%Y Cf. A321531, A321532.

%K nonn,more

%O 1,5

%A _Peter Kagey_, Nov 12 2018