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A319476 a(n) is the minimum number of distinct distances between n non-attacking rooks on an n X n chessboard.

%I A319476 #49 Dec 30 2018 12:08:16
%S A319476 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 A319476 a(n) is the minimum number of distinct distances between n non-attacking rooks on an n X n chessboard.
%C A319476 a(n) <= n - 1, which is the number of distinct distances the rooks are placed along a diagonal.
%C A319476 Conjecture: a(n^2) = A047800(n-1) - 1. - _Peter Kagey_, Nov 02 2018
%H A319476 Giovanni Resta, <a href="/A319476/a319476.pdf">Illustration of a(3)-a(14)</a>
%e A319476 For n = 7 a board with a(7) = 5 distinct distances is
%e A319476   +---+---+---+---+---+---+---+
%e A319476 7 |   |   | * |   |   |   |   |
%e A319476   +---+---+---+---+---+---+---+
%e A319476 6 |   |   |   |   |   | * |   |
%e A319476   +---+---+---+---+---+---+---+
%e A319476 5 | * |   |   |   |   |   |   |
%e A319476   +---+---+---+---+---+---+---+
%e A319476 4 |   |   |   | * |   |   |   |
%e A319476   +---+---+---+---+---+---+---+.
%e A319476 3 |   |   |   |   |   |   | * |
%e A319476   +---+---+---+---+---+---+---+
%e A319476 2 |   | * |   |   |   |   |   |
%e A319476   +---+---+---+---+---+---+---+
%e A319476 1 |   |   |   |   | * |   |   |
%e A319476   +---+---+---+---+---+---+---+
%e A319476     A   B   C   D   E   F   G
%e A319476 The distances between pairs of points are:
%e A319476 1)   sqrt(10) (e.g., A5 to B2),
%e A319476 2) 2*sqrt(2)  (e.g., A5 to C7),
%e A319476 3) 4*sqrt(2)  (e.g., B2 to F6),
%e A319476 4) 2*sqrt(10) (e.g., A5 to G3), and
%e A319476 5)   sqrt(26) (e.g., A5 to F6).
%Y A319476 Cf. A008404, A319476, A320575, A320576, A320448, A320573, A320574.
%K A319476 nonn,more
%O A319476 1,3
%A A319476 _Peter Kagey_, Oct 12 2018
%E A319476 a(11)-a(14) from _Giovanni Resta_, Oct 17 2018
%E A319476 a(15)-a(25) from _Bert Dobbelaere_, Dec 30 2018