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.

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

1,4

References

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

Links

Table of n, a(n) for n=1..61.

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)

Example

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)

Crossrefs

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

Sequence in context: A078117 A256073 A032423 * A317770 A154685 A068591

Adjacent sequences: A063721 A063722 A063723 * A063725 A063726 A063727

Keyword

easy,nonn

Author

Jud McCranie, Aug 11 2001

Status

approved