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Search: id:A037223
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| A037223 |
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Number of solutions to non-attacking rooks problem on n X n board that are invariant under 180 degree rotation. |
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9
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| 1, 1, 2, 2, 8, 8, 48, 48, 384, 384, 3840, 3840, 46080, 46080, 645120, 645120, 10321920, 10321920, 185794560, 185794560, 3715891200, 3715891200, 81749606400, 81749606400, 1961990553600, 1961990553600, 51011754393600, 51011754393600
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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This is just A000165 doubled up. Normally such sequences do not get their own entry in the OEIS. This is an exception. - N. J. A. Sloane (njas(AT)research.att.com), Sep 23 2006
Also the number of permutations of (1,2,3,...,n) for which the reverse of the inverse is the same as the inverse of the reverse. - Ian Duff (ianfduff(AT)yahoo.co.uk), Mar 09 2007
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REFERENCES
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E. Lucas, Theorie des nombres, Gauthiers-Villars, Paris, 1891, Vol 1, p. 221.
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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M. Szabo, Non-attacking Queens Problem Page
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FORMULA
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a(2n) = a(2n+1) = (n)!*2^(n).
Exponential generating function: 1+x+(1+x+x^2)*exp(x^2/2)*sqrt(Pi/2)*erf(x/sqrt(2)), where erf denotes the error function. - Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Nov 01 2002
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. A000165, A033148, A037224, A032522, A037223.
Sequence in context: A007083 A144060 A016119 this_sequence A066988 A100384 A000023
Adjacent sequences: A037220 A037221 A037222 this_sequence A037224 A037225 A037226
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KEYWORD
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nonn
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AUTHOR
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Miklos SZABO (mike(AT)ludens.elte.hu)
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EXTENSIONS
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More terms from Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Nov 01 2002
Edited by N. J. A. Sloane (njas(AT)research.att.com), Sep 23 2006
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