Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.
%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