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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

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

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 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

.

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

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Last modified March 19 17:21 EDT 2019. Contains 321330 sequences. (Running on oeis4.)