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A321531
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a(n) is the maximum number of distinct directions between n non-attacking rooks on an n X n chessboard.
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2
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OFFSET
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1,3
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COMMENTS
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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.
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LINKS
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EXAMPLE
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For n = 5, a 5 X 5 board with a(5) = 6 distinct directions is
+---+---+---+---+---+
5| X | | | | |
+---+---+---+---+---+
4| | | X | | |
+---+---+---+---+---+
3| | | | X | |
+---+---+---+---+---+
2| | | | | X |
+---+---+---+---+---+
1| | x | | | |
+---+---+---+---+---+
A B C D E
Where the six distinct directions are:
1) 1:4 by (A5,B1).
2) 1:2 by (A5,C4).
3) 2:3 by (A5,D3).
4) 3:4 by (A5,E2).
5) 1:3 by (B1,C4) and (B1,E2).
6) 1:1 by (B1,D3), (C4,D3), (C4,E2), and (D3,E2).
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CROSSREFS
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Cf. A320448 (analogous with distance instead of direction).
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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