Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the 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