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Search: id:A000684
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| A000684 |
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Number of colored labeled n-node graphs with 2 interchangeable colors.
(Formerly M2954 N1192)
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+0
1
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| 1, 3, 13, 81, 721, 9153, 165313, 4244481, 154732801, 8005686273, 587435092993, 61116916981761, 9011561121239041, 1882834327457349633, 557257804202631217153, 233610656002563147038721, 138681207656726645785559041
(list; graph; listen)
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OFFSET
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1,2
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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).
F. Harary and R. W. Robinson, Labeled bipartite blocks, Canad. J. Math., 31 (1979), 60-68.
D. A. Klarner, The number of graded partially ordered sets, J. Combin. Theory, 6 (1969), 12-19.
A. Nymeyer and R. W. Robinson, ``Tabulation of the Numbers of Labeled Bipartite Blocks and Related Classes of Bicolored Graphs,'' unpublished manuscript, 1982.
R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1976.
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LINKS
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R. W. Robinson, Table of n, a(n) for n = 1..32
S. R. Finch, Bipartite, k-colorable and k-colored graphs (2*A000684)
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FORMULA
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G.f.: A(x) = Sum_{n>=1} x^n/(1 - 2^n*x)^n. [From Paul D. Hanna (pauldhanna(AT)juno.com), Sep 14 2009]
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PROGRAM
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(PARI) a(n)=polcoeff(sum(k=1, n, x^k/(1-2^k*x +x*O(x^n))^k), n) [From Paul D. Hanna (pauldhanna(AT)juno.com), Sep 14 2009]
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CROSSREFS
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2 * A000683(n) + 1. Cf. A058872.
Sequence in context: A135921 A005923 A089461 this_sequence A057993 A000904 A135743
Adjacent sequences: A000681 A000682 A000683 this_sequence A000685 A000686 A000687
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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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a(15) onwards added by N. J. A. Sloane (njas(AT)research.att.com), Oct 19 2006 from the Robinson reference
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