A319476 - OEIS

%I #49 Dec 30 2018 12:08:16

%S 0,1,2,2,3,5,5,6,5,7,9,7,8,11,13,9,11,14,16,17,19,21,21,14,14

%N a(n) is the minimum number of distinct distances between n non-attacking rooks on an n X n chessboard.

%C a(n) <= n - 1, which is the number of distinct distances the rooks are placed along a diagonal.

%C Conjecture: a(n^2) = A047800(n-1) - 1. - _Peter Kagey_, Nov 02 2018

%H Giovanni Resta, <a href="/A319476/a319476.pdf">Illustration of a(3)-a(14)</a>

%e For n = 7 a board with a(7) = 5 distinct distances is

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

%e 7 |   |   | * |   |   |   |   |

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

%e 6 |   |   |   |   |   | * |   |

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

%e 5 | * |   |   |   |   |   |   |

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

%e 4 |   |   |   | * |   |   |   |

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

%e 3 |   |   |   |   |   |   | * |

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

%e 2 |   | * |   |   |   |   |   |

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

%e 1 |   |   |   |   | * |   |   |

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

%e     A   B   C   D   E   F   G

%e The distances between pairs of points are:

%e 1)   sqrt(10) (e.g., A5 to B2),

%e 2) 2*sqrt(2)  (e.g., A5 to C7),

%e 3) 4*sqrt(2)  (e.g., B2 to F6),

%e 4) 2*sqrt(10) (e.g., A5 to G3), and

%e 5)   sqrt(26) (e.g., A5 to F6).

%Y Cf. A008404, A319476, A320575, A320576, A320448, A320573, A320574.

%K nonn,more

%O 1,3

%A _Peter Kagey_, Oct 12 2018

%E a(11)-a(14) from _Giovanni Resta_, Oct 17 2018

%E a(15)-a(25) from _Bert Dobbelaere_, Dec 30 2018