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.

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A051757 Consider problem of placing A051754(n) queens on an n X n board so that each queen attacks precisely 1 other. Sequence gives number of solutions up to square symmetry.

Original entry on oeis.org

2, 7, 5, 93, 2, 149, 49, 1, 12897, 2238
Offset: 2

Views

Author

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

Keywords

Comments

When n is a multiple of 3, the bound of 2[2n/3] queens is so tight that in solutions with that number of queens, all attacks must be along rows or columns, making solutions rare. - Jud McCranie

References

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

Crossrefs

Cf. A051754-A051759, A051567-A051571, A019654.

Extensions

More terms from Jud McCranie, Aug 14 2001

A051758 Consider problem of placing A051755(n) queens on an n X n board so that each queen attacks precisely 2 others. Sequence gives number of solutions up to square symmetry.

Original entry on oeis.org

1, 4, 2, 1, 1, 5, 2, 15
Offset: 2

Views

Author

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

Keywords

Crossrefs

Cf. A051754-A051759, A051567-A051571, A019654.

Extensions

a(9) from Sean A. Irvine, Oct 05 2021

A063724 Consider problem of placing N queens on an n X n board so that each queen attacks precisely 4 others. Sequence gives maximal number of queens.

Original entry on oeis.org

0, 0, 0, 8, 11, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87, 90, 93, 96, 99, 102, 105, 108, 111, 114, 117, 120, 123, 126, 129, 132, 135, 138, 141, 144, 147, 150, 153, 156, 159, 162, 165, 168, 171, 174, 177, 180
Offset: 1

Views

Author

Jud McCranie, Aug 11 2001

Keywords

Examples

			Examples from _Sean A. Irvine_, Mar 31 2019: (Start)
a(4) = 8:
.QQ.
Q..Q
Q..Q
.QQ.
a(5) = 11:
.Q.Q.
Q...Q
Q...Q
Q...Q
.QQQ.
a(6) = 15:
.Q..Q.
Q...QQ
Q.Q...
Q....Q
Q....Q
.QQQQ.
(End)

References

  • Peter Hayes, A Problem of Chess Queens, Journal of Recreational Mathematics, 24(4), 1992, 264-271.

Crossrefs

Cf. A051754-A051759, A051567-A051571, A019654.

Formula

a(1)=a(2)=a(3)=0, a(4)=8, a(5)=11, a(n) = 3n - 3 for n >= 6.
From Colin Barker, Apr 13 2012: (Start)
a(n) = 2*a(n-1) - a(n-2) for n >= 8.
G.f.: x^4*(8 - 5*x + x^2 - x^3)/(1-x)^2. (End)
Previous Showing 11-13 of 13 results.

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

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