A051570 -id:A051570 - cp's OEIS frontend

A051571 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.

Original entry on oeis.org

0, 0, 0, 1, 3, 40, 615, 16573

Offset: 3

N. J. A. Sloane

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

Cf. A051567-A051570, A051754-A051759, A019654.

Probably an incorrect version of A019654.

A051756 Consider the problem of placing N queens on an n X n board so that each queen attacks precisely 3 others. Sequence gives maximal number of queens.

Original entry on oeis.org

4, 6, 8, 10, 12, 16, 18, 20, 22, 24, 28, 30, 32, 34, 36, 40, 42, 44, 46, 48, 52, 54, 56, 58, 60, 64, 66, 68, 70, 72, 76, 78, 80, 82, 84, 88, 90, 92, 94, 96, 100, 102, 104, 106, 108, 112, 114, 116, 118, 120, 124, 126, 128, 130, 132, 136, 138, 140, 142, 144

Offset: 2

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

a(n) <= 2[(6n-2)/5]. - Jud McCranie, Aug 12 2001

Conjecture: a(n) = 2[(6n-2)/5] for n >= 2; verified up to n = 100. - Alexander D. Healy, Feb 11 2024

			Examples from _R. J. Mathar_, May 01 2006: (Start)
==== n = 3
6 queens:
Q Q Q
Q - -
Q - Q
6 queens:
Q Q Q
- - -
Q Q Q
==== n = 4
8 queens:
Q Q Q Q
Q - - -
Q - - -
Q - - Q
8 queens:
Q Q Q Q
Q - - -
- - Q -
Q - - Q
8 queens:
Q Q Q Q
- - - -
- - - -
Q Q Q Q
8 queens:
Q Q - Q
- Q - -
- - Q -
Q - Q Q
==== n = 7
16 queens:
Q Q Q - Q - Q
- - - - - - Q
- - - Q - - -
Q - - - - - Q
- - - Q - - -
Q - - - - - -
Q - Q - Q Q Q
16 queens:
Q Q Q - - Q Q
- - - Q - - -
- - - - - - Q
Q - - - - - Q
Q - - - - - -
- - - Q - - -
Q Q - - Q Q Q
(End)

Martin Gardner, The Last Recreations, Copernicus, NY, 1997, 274-283.
Peter Hayes, A Problem of Chess Queens, Journal of Recreational Mathematics, Baywood, 24(4), 1992, 264-271.

Alexander D. Healy, Examples of optimal placements for n <= 61

Cf. A051754, A051755, A051757, A051758, A051759, A051567, A051568, A051569, A051570, A051571, A019654.

More terms from Jud McCranie, Aug 12 2001

a(10)-a(61) from Alexander D. Healy, Feb 11 2024

cp's OEIS Frontend

A051571 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.

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