A063724 -id:A063724 - cp's OEIS frontend

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.

0, 1, 1, 1, 3, 40, 655, 16573

Offset: 3

N. J. A. Sloane, Oct 03 2002

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
Values for a(9) onwards currently unverified. - Sean A. Irvine, Apr 05 2019

M. Gardner, The Last Recreations, Springer, 1997, p. 282.
M. Gardner, The Colossal Book of Mathematics, 2001, p. 209.

Sean A. Irvine, Solutions for n<=8
Eric Weisstein's World of Mathematics, Queens Problem [From Claudio (lordofchaos000(AT)hotmail.com), May 31 2010]

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

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

A051754 Consider problem of placing N queens on an n X n board so that each queen attacks precisely 1 other. Sequence gives maximal number of queens.

Original entry on oeis.org

2, 2, 4, 4, 8, 8, 10, 12, 12, 14, 16, 16, 18, 20, 20, 22, 24, 24, 26, 28, 28, 30, 32, 32, 34, 36, 36, 38, 40, 40, 42, 44, 44, 46, 48, 48, 50, 52, 52, 54, 56, 56, 58, 60, 60, 62, 64, 64, 66, 68, 68, 70, 72, 72, 74, 76, 76, 78, 80, 80, 82, 84, 84, 86

Offset: 2

Robert Trent (trentrd(AT)hotmail.com), Aug 23 2000

2*[2n/3] is an upper bound for a(n). - Jud McCranie, Aug 12 2001
This bound is achieved for n=2, 4 and 6-65.
Conjecture: a(n) = 2*[2n/3] for n >= 6. - Alexander D. Healy, Feb 10 2024

Martin Gardner, The Last Recreations, Copernicus, NY, 1997, 274-283.

Alexander D. Healy, Examples of optimal placements for n <= 65

Cf. A051755-A051759, A051567-A051571, A019654, A063724.

a(12)-a(65) from Alexander D. Healy, Feb 10 2024

cp's OEIS Frontend

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.

Views

Author

Keywords

Comments

References

Links

Crossrefs

Extensions