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A171760
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The maximum number of sets of n queens which can be placed on an n X n chessboard such that no queen attacks another queen in the same set.
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1
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0, 1, 0, 0, 2, 5, 4, 7, 6, 7, 8, 11, 12, 13
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OFFSET
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0,5
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COMMENTS
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a(n) is nonzero for n >= 4 (there is always at least one solution to the n-queens problem). a(n) <= n (because n sets of n queens fill up the board). a(n) = n if n = 1 or 5 (mod 6). Further known terms include 0,1,0,0,2,5,_,7,_,_,_,11,12,13, with the missing terms being greater than 0 and less than n.
a(n) is at least two for all even n >= 4 since a solution and its reflection will fit on the same board. - Charlie Neder, Jul 24 2018
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LINKS
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Table of n, a(n) for n=0..13.
Giovanni Resta, A C program for computing a(1)-a(11)
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EXAMPLE
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a(4) = 2 because there are only two solutions to the 4-queens problem and they can both fit on the same board:
0 1 2 0
2 0 0 1
1 0 0 2
0 2 1 0
a(8) = 6 since at least 6 solutions to the 8-queens problem can fit on the same board but 7 solutions can't:
3 0 5 2 1 6 0 4
0 1 4 0 5 3 2 6
4 6 0 1 2 0 5 3
5 2 3 6 0 4 1 0
6 4 1 5 0 2 3 0
2 5 0 3 4 0 6 1
0 3 2 0 6 1 4 5
1 0 6 4 3 5 0 2
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a(9) = 7
7 5 6 3 1 . . 2 4
6 3 . 4 2 7 1 . 5
. . 2 7 5 6 3 4 1
4 7 5 1 . 2 . 6 3
3 1 4 . 6 . 7 5 2
. 6 . 5 3 4 2 1 7
2 4 7 6 . 1 5 3 .
5 . 1 2 7 3 4 . 6
1 2 3 . 4 5 6 7 .
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a(10) = 8
3 4 2 8 . . 1 7 5 6
6 . 7 1 5 4 8 2 . 3
. 1 5 6 7 2 3 4 8 .
2 8 4 . 3 6 . 5 1 7
7 . 6 5 1 8 4 3 . 2
8 3 . 4 2 7 5 . 6 1
5 6 8 7 . . 2 1 3 4
4 7 3 . 8 1 . 6 2 5
. 5 1 2 6 3 7 8 4 .
1 2 . 3 4 5 6 . 7 8
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CROSSREFS
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Cf. A000170.
Sequence in context: A102513 A100116 A107921 * A085801 A023843 A153990
Adjacent sequences: A171757 A171758 A171759 * A171761 A171762 A171763
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KEYWORD
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more,nonn
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AUTHOR
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Howard A. Landman, Dec 17 2009
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EXTENSIONS
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a(6) and known a(7) added by Charlie Neder, Jul 24 2018
a(8)-a(10) and known a(11)-a(13) from Giovanni Resta, Jul 26 2018
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STATUS
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approved
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