

A171760


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.


1



0, 1, 0, 0, 2, 5, 4, 7, 6, 7, 8, 11, 12, 13
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OFFSET

0,5


COMMENTS

a(n) is nonzero for n >= 4 (there is always at least one solution to the nqueens 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


LINKS

Table of n, a(n) for n=0..13.
Giovanni Resta, A C program for computing a(1)a(11)


EXAMPLE

a(4) = 2 because there are only two solutions to the 4queens 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 8queens 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
.
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 .
.
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


CROSSREFS

Cf. A000170.
Sequence in context: A102513 A100116 A107921 * A085801 A023843 A153990
Adjacent sequences: A171757 A171758 A171759 * A171761 A171762 A171763


KEYWORD

more,nonn


AUTHOR

Howard A. Landman, Dec 17 2009


EXTENSIONS

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


STATUS

approved



