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Search: id:A061989
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| A061989 |
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Number of ways to place 3 nonattacking queens on a 3 X n board. |
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7
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| 0, 0, 0, 0, 4, 14, 36, 76, 140, 234, 364, 536, 756, 1030, 1364, 1764, 2236, 2786, 3420, 4144, 4964, 5886, 6916, 8060, 9324, 10714, 12236, 13896, 15700, 17654, 19764, 22036, 24476, 27090, 29884, 32864, 36036, 39406, 42980, 46764, 50764
(list; graph; listen)
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OFFSET
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0,5
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LINKS
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V. Kotesovec, Ways of placing non-attacking queens and kings..., part of "Between chessboard and computer", 1996, pp. 204 - 206.
E. Lucas, Recreations mathematiques I, Albert Blanchard, Paris, 1992, p. 231.
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FORMULA
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G.f.: 2*x^4*(2*x^2-x+2)/(x-1)^4. Recurrence: a(n)=4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4), n >= 7. Explicit formula (H. Tarry, 1890): a(n)=(n-3)*(n^2-6*n+12), n >= 3.
(4, 14, 36...) is the binomial transform of row 4 of A117937: (4, 10, 12, 6). - Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 09 2006
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CROSSREFS
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Cf. A061990.
Essentially the same as A079908.
Cf. A117937.
Sequence in context: A099586 A063258 A011852 this_sequence A079908 A038164 A034528
Adjacent sequences: A061986 A061987 A061988 this_sequence A061990 A061991 A061992
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KEYWORD
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nonn
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AUTHOR
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Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), May 29 2001
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