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%I #11 Dec 14 2018 19:49:35
%S 0,1,2,4,6,8,11,14,18,23
%N a(n) is the maximum number of distinct directions between n non-attacking rooks on an n X n chessboard.
%C Directions are determined up to scaling and dihedral action of the square, as in (m,k)-riders. For example, the moves (1,2) and (2,-4) are considered to have the same direction.
%e For n = 5, a 5 X 5 board with a(5) = 6 distinct directions is
%e +---+---+---+---+---+
%e 5| X | | | | |
%e +---+---+---+---+---+
%e 4| | | X | | |
%e +---+---+---+---+---+
%e 3| | | | X | |
%e +---+---+---+---+---+
%e 2| | | | | X |
%e +---+---+---+---+---+
%e 1| | x | | | |
%e +---+---+---+---+---+
%e A B C D E
%e Where the six distinct directions are:
%e 1) 1:4 by (A5,B1).
%e 2) 1:2 by (A5,C4).
%e 3) 2:3 by (A5,D3).
%e 4) 3:4 by (A5,E2).
%e 5) 1:3 by (B1,C4) and (B1,E2).
%e 6) 1:1 by (B1,D3), (C4,D3), (C4,E2), and (D3,E2).
%Y Cf. A320448 (analogous with distance instead of direction).
%K nonn,more
%O 1,3
%A _Peter Kagey_, Nov 12 2018
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