A019654 Consider problem of placing N queens on an n X n board so that each queen attacks precisely k others. Here k=4 and sequence gives number of different solutions when N takes its maximal value.

1, 1, 1, 1, 1, 1, 3, 40, 615, 16573, 491734

Offset

1,7

Comments

I would also like to get the sequences that give the maximal value of N.

Maximal values given by A063724. - Sean A. Irvine, Mar 31 2019

a(9) onwards recalculated in two different ways. a(9)-a(10) calculated using CP-SAT constraint solver. a(9)-a(11) calculated using depth-first search. - Martin Fuller, Jan 04 2026

References

Martin Gardner, The Last Recreations, Springer, 1997, p. 282.

Martin Gardner, The Colossal Book of Mathematics, 2001, p. 209.

Links

Table of n, a(n) for n=1..11.

Martin Fuller, Python program

Sean A. Irvine, Solutions for n<=8

Eric Weisstein's World of Mathematics, Queens Problem [From Claudio (lordofchaos000(AT)hotmail.com), May 31 2010]

Prog

(Python + CP-SAT) # See Fuller link.

Crossrefs

Cf. A051567-A051571, A051754-A051759, A063724.

Sequence in context: A005724 A215196 A093376 * A051571 A361069 A327070

Adjacent sequences: A019651 A019652 A019653 * A019655 A019656 A019657

Keyword

nonn,nice,more

Author

N. J. A. Sloane, Oct 03 2002

Extensions

I am not certain this description is correct, nor how rigorous the results are.

a(4) and a(5) changed to 1 and irrelevant comment removed by Sean A. Irvine, Apr 02 2019

a(1)=a(2)=a(3)=1 (with N=0), a(9) corrected, a(10) confirmed and a(11) added by Martin Fuller, Jan 04 2026

Status

approved