cp's OEIS Frontend

A320448 a(n) is the maximum number of distinct distances between n non-attacking rooks on an n X n chessboard.

%I A320448 #26 Jan 01 2019 06:40:06
%S A320448 0,1,2,4,8,11,15,20,25,31,37,44,51,59,68
%N A320448 a(n) is the maximum number of distinct distances between n non-attacking rooks on an n X n chessboard.
%C A320448 A319476(n) <= a(n) <= n(n-1)/2.
%H A320448 Giovanni Resta, <a href="/A320448/a320448.pdf">Illustration of a(3)-a(14)</a>
%e A320448 For n = 5 a placement of five rooks on a 5 X 5 board with a(5) = 8 distinct distances is:
%e A320448   +---+---+---+---+---+
%e A320448 5 |   | * |   |   |   |
%e A320448   +---+---+---+---+---+
%e A320448 4 | * |   |   |   |   |
%e A320448   +---+---+---+---+---+
%e A320448 3 |   |   |   |   | * |
%e A320448   +---+---+---+---+---+.
%e A320448 2 |   |   | * |   |   |
%e A320448   +---+---+---+---+---+
%e A320448 1 |   |   |   | * |   |
%e A320448   +---+---+---+---+---+
%e A320448     A   B   C   D   E
%e A320448 The distances between pairs of pieces are:
%e A320448 1)   sqrt(2)  (A4 to B5 and C2 to D1)
%e A320448 2) 2*sqrt(2)  (A4 to C2)
%e A320448 3) 3*sqrt(2)  (A4 to D1)
%e A320448 4)   sqrt(17) (A4 to E3)
%e A320448 5)   sqrt(10) (B5 to C2)
%e A320448 6) 2*sqrt(5)  (B5 to D1)
%e A320448 7)   sqrt(13) (B5 to E3)
%e A320448 8)   sqrt(5)  (C2 to E3 and D1 to E3)
%Y A320448 Cf. A008404, A319476, A320575, A320576, A320448, A320573, A320574.
%K A320448 nonn,more,hard
%O A320448 1,3
%A A320448 _Peter Kagey_, Oct 12 2018
%E A320448 a(11)-a(14) from _Giovanni Resta_, Oct 17 2018
%E A320448 a(15) from _Bert Dobbelaere_, Jan 01 2019