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

Author

Jud McCranie, Aug 11 2001

Keywords

• easy
• nonn

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)