cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-2 of 2 results.

A051759 Consider the problem of placing A051756(n) queens on an n X n board so that each queen attacks precisely 3 others. Sequence gives number of solutions up to square symmetry.

Original entry on oeis.org

1, 2, 4, 31, 307, 2, 9, 755
Offset: 2

Views

Author

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

Keywords

Comments

A051569 (taken from the Martin Gardner references) is another version of this sequence. - N. J. A. Sloane, May 22 2014

References

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

Links

Crossrefs

Cf. A051754-A051758, A051567-A051571, A019654.

Extensions

a(8)-a(9) from Sean A. Irvine, Oct 01 2021

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

Views

Author

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

Keywords

Comments

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

			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)

References

  • 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.

Links

Crossrefs

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

Extensions

More terms from Jud McCranie, Aug 12 2001
a(10)-a(61) from Alexander D. Healy, Feb 11 2024
Showing 1-2 of 2 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.