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Search: id:A000899
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| A000899 |
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Number of solutions to the rook problem on an n X n board having a certain symmetry group (see Robinson for details).
(Formerly M4645 N1987)
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+0
3
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| 0, 0, 0, 1, 9, 70, 571, 4820, 44676, 450824, 4980274, 59834748, 778230060, 10896609768, 163456629604, 2615335902176, 44460874280032, 800296440705472, 15205636325496568, 304112744618157872, 6386367741011250672
(list; graph; listen)
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OFFSET
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1,5
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
L. C. Larson, The number of essentially different nonattacking rook arrangements, J. Recreat. Math., 7 (No. 3, 1974), circa pages 180-181.
R. W. Robinson, Counting arrangements of bishops, pp. 198-214 of Combinatorial Mathematics IV (Adelaide 1975), Lect. Notes Math., 560 (1976).
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LINKS
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T. D. Noe, Table of n, a(n) for n = 1..200
E. Lucas, Th\'{e}orie des Nombres. Gauthier-Villars, Paris, 1891, Vol. 1, p. 222.
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FORMULA
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a(n)=(A000142(n)-2*A000085(n)-A037223(n)+2*A000898(floor(n/2)))/8 (all of which have explicit formulae).
For asymptotics see the Robinson paper.
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MAPLE
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For Maple program see A000903.
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CROSSREFS
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Cf. A000900.
Sequence in context: A110201 A045739 A098205 this_sequence A156705 A081900 A164551
Adjacent sequences: A000896 A000897 A000898 this_sequence A000900 A000901 A000902
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KEYWORD
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nonn,nice,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), May 09 2000
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