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A063724
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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.
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1
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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
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OFFSET
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1,4
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REFERENCES
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Peter Hayes, A Problem of Chess Queens, Journal of Recreational Mathematics, 24(4), 1992, 264-271.
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LINKS
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Table of n, a(n) for n=1..61.
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FORMULA
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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)
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EXAMPLE
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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)
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CROSSREFS
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Cf. A051754-A051759, A051567-A051571, A019654.
Sequence in context: A078117 A256073 A032423 * A317770 A154685 A068591
Adjacent sequences: A063721 A063722 A063723 * A063725 A063726 A063727
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KEYWORD
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easy,nonn
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AUTHOR
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Jud McCranie, Aug 11 2001
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STATUS
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approved
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