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A000900
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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 M1964 N0777)
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4
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0, 0, 0, 1, 2, 10, 28, 106, 344, 1272, 4592, 17692, 69384, 283560, 1191984, 5171512, 23087168, 105883456, 498572416, 2404766224, 11878871456, 59975885856, 309439708352, 1628919330208, 8746079933568, 47840206525056
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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REFERENCES
| 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).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| T. D. Noe, Table of n, a(n) for n = 0..200
E. Lucas, Th\'{e}orie des Nombres. Gauthier-Villars, Paris, 1891, Vol. 1, p. 222.
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FORMULA
| a(n)=(A000085(n)-A000898(int(n/2)))/2
For asymptotics see the Robinson paper.
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MAPLE
| For Maple program see A000903.
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MATHEMATICA
| a85[n_] := Sum[ (2k)!/k!/2^k Binomial[n, 2k], {k, 0, n/2}]; a898[n_] := Sum[ 2^k*StirlingS1[n, k]*BellB[k], {k, 0, n}]; a[n_] := (a85[n] - a898[Floor[n/2]])/2; a[1] = 0; Table[a[n], {n, 0, 25}] (* From Jean-François Alcover, Dec 13 2011, after formula *)
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CROSSREFS
| Sequence in context: A053594 A006331 A104657 * A124023 A127921 A106184
Adjacent sequences: A000897 A000898 A000899 * A000901 A000902 A000903
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), May 09 2000
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