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A000719
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Number of disconnected graphs with n nodes.
(Formerly M1452 N0574)
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5
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0, 0, 1, 2, 5, 13, 44, 191, 1229, 13588, 288597, 12297299, 1031342116, 166123498733, 50668194387427, 29104827043066808, 31455591302381718651, 64032471448906164191208, 245999896712611657677614268
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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REFERENCES
| 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).
M. L. Stein and P. R. Stein, Enumeration of Linear Graphs and Connected Linear Graphs up to $p = 18$ Points. Report LA-3775, Los Alamos Scientific Laboratory of the University of California, Los Alamos, NM, Oct 1967.
F. Harary, The number of linear, directed, rooted and connected graphs, Trans. Amer. Math. Soc., 78 (1955), 445-463.
R. C. Read and R. J. Wilson, An Atlas of Graphs, Oxford, 1998.
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LINKS
| David Wasserman, Table of n, a(n) for n = 0..30
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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MATHEMATICA
| << "Combinatorica`"; max = 18; A000088 = Table[ NumberOfGraphs[n], {n, 0, max}]; f[x_] = 1 - Product[ 1/(1 - x^k)^b[k], {k, 1, max}]; b[0] = b[1] = b[2] = 1; coes = CoefficientList[ Series[ f[x], {x, 0, max}], x]; sol = First[ Solve[ Thread[ Rest[ coes + A000088 ] == 0]]]; a[n_] := a[n] = A000088[[n+1]] - b[n] /. sol; a[0] = a[1] = 0; Table[a[n], {n, 0, max}] (* From Jean-François Alcover, Nov 24 2011 *)
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CROSSREFS
| Equals (A000088) minus (A001349).
Sequence in context: A192745 A119533 A066740 * A149875 A085632 A111563
Adjacent sequences: A000716 A000717 A000718 * A000720 A000721 A000722
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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 Christian Bower (bowerc(AT)usa.net). Further terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 14 2000.
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