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Search: id:A000986
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| A000986 |
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Number of n X n symmetric matrices with (0,1) entries and all row sums 2.
(Formerly M3548 N1437)
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+0
8
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| 1, 0, 1, 4, 18, 112, 820, 6912, 66178, 708256, 8372754, 108306280, 1521077404, 23041655136, 374385141832, 6493515450688, 119724090206940, 2337913445039488, 48195668439235612, 1045828865817825264, 23826258064972682776, 568556266922455167040
(list; graph; listen)
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OFFSET
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0,4
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REFERENCES
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H. Gupta, Enumeration of symmetric matrices, Duke Math. J., 35 (1968), 653-659.
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).
R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Example 5.2.8.
Tan and S. Gao, Enumeration of (0,1)-Symmetric Matrices,submitted [From Shanzhen Gao (sgao2(AT)fau.edu), Jun 05 2009]
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..100
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FORMULA
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E.g.f.: (1-x)^(-1/2)*exp(-x-x^2/4 + x/((2*(1-x)))).
$\dsum\limits_{a_{1}=0}^{n}\dsum\limits_{c=0}^{\min \{a_{1},n-a_{1}\}}\dsum\limits_{b=0}^{\lfloor (n-a_{1}-c)/2\rfloor }\frac{% (-1)^{(n-a_{1}-2b-c)+b}n!(2a_{1})!}{% 2^{n+a_{1}-2c}a_{1}!(n-a_{1}-2b-c)!b!(2c)!(a_{1}-c)!}$ [From Shanzhen Gao (sgao2(AT)fau.edu), Jun 05 2009]
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CROSSREFS
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Cf. A000985.
Adjacent sequences: A000983 A000984 A000985 this_sequence A000987 A000988 A000989
Sequence in context: A060223 A144085 A003708 this_sequence A143920 A113356 A062805
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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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