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A058528
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Number of n X n (0,1) matrices with all column and row sums equal to 4.
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4
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1, 0, 0, 0, 1, 120, 67950, 68938800, 116963796250, 315031400802720, 1289144584143523800, 7722015017013984456000, 65599839591251908982712750, 769237071909157579108571190000, 12163525741347497524178307740904300
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,6
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COMMENTS
| Further terms generated by a Mathematica program written by Gordon G. Cash, who thanks B. R. Perez-Salvador, Universidad Autonoma Metropolitana Unidad Iztapalapa, Mexico, for providing the algorithm on which this program was based.
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REFERENCES
| B. R. Perez-Salvador, S. de los Cobos Silva, M. A. Gutierrez-Andrade and A. Torres-Chazaro, A Reduced Formula for Precise Numbers of (0,1) Matrices in a(R,S), Disc. Math., 2002, 256, 361-372.
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LINKS
| Vladeta Jovovic (vladeta(AT)eunet.rs), Nov 12 2006, Table of n, a(n) for n = 0..31
Index entries for sequences related to binary matrices
B. D. McKay, 0-1 matrices with constant row and column sums
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FORMULA
| a(n)=24^{-n} sum_{alpha +beta + gamma + mu + u =n}frac{3^{ gamma }(-6)^{beta +u }8^{ mu }(n!)^{2}(4alpha +2 gamma + mu )!(beta +2 gamma )!}{alpha!beta! gamma! mu!u!} sum_{i=0}^{ floor (beta +2 gamma )/2 }frac{1}{24^{alpha - gamma +i}2^{beta +2 gamma -i}i!(beta +2 gamma -2i)!(alpha - gamma +i)!} - Shanzhen Gao (sgao2(AT)fau.edu), Nov 07 2007
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EXAMPLE
| a(4)=1 because there is only one possible 4 X 4 (0,1) matrix with all row and column sums equal to 4, the matrix of all 1's. a(5)=120=5! because there are 5X4X3X2X1 ways of placing a zero in each successive column (row) so that it is not in the same row (column) as any previously placed.
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CROSSREFS
| Cf. A001499, A001501.
Sequence in context: A109897 A074653 A065961 * A001421 A107446 A184887
Adjacent sequences: A058525 A058526 A058527 * A058529 A058530 A058531
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KEYWORD
| nonn
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AUTHOR
| David desJardins (david(AT)desjardins.org), Dec 22 2000
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EXTENSIONS
| More terms from Gordon G. Cash (cash.gordon(AT)epa.gov), Oct 22 2002
More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Nov 12 2006
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