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a(n) is the maximum number of distinct distances between n non-attacking rooks on an n X n chessboard.
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%I #26 Jan 01 2019 06:40:06

%S 0,1,2,4,8,11,15,20,25,31,37,44,51,59,68

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

%C A319476(n) <= a(n) <= n(n-1)/2.

%H Giovanni Resta, <a href="/A320448/a320448.pdf">Illustration of a(3)-a(14)</a>

%e For n = 5 a placement of five rooks on a 5 X 5 board with a(5) = 8 distinct distances is:

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

%e 5 | | * | | | |

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

%e 4 | * | | | | |

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

%e 3 | | | | | * |

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

%e 2 | | | * | | |

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

%e 1 | | | | * | |

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

%e A B C D E

%e The distances between pairs of pieces are:

%e 1) sqrt(2) (A4 to B5 and C2 to D1)

%e 2) 2*sqrt(2) (A4 to C2)

%e 3) 3*sqrt(2) (A4 to D1)

%e 4) sqrt(17) (A4 to E3)

%e 5) sqrt(10) (B5 to C2)

%e 6) 2*sqrt(5) (B5 to D1)

%e 7) sqrt(13) (B5 to E3)

%e 8) sqrt(5) (C2 to E3 and D1 to E3)

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

%K nonn,more,hard

%O 1,3

%A _Peter Kagey_, Oct 12 2018

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

%E a(15) from _Bert Dobbelaere_, Jan 01 2019