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A000719
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Number of disconnected graphs with n nodes.
(Formerly M1452 N0574)
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15
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0, 0, 1, 2, 5, 13, 44, 191, 1229, 13588, 288597, 12297299, 1031342116, 166123498733, 50668194387427, 29104827043066808, 31455591302381718651, 64032471448906164191208, 245999896712611657677614268, 1787823725136869060356731751124
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OFFSET
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0,4
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COMMENTS
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a(n) is also the number of simple unlabeled graphs on n+1 nodes with diameter 2 and connectivity 1. - Geoffrey Critzer, Oct 23 2016
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REFERENCES
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R. C. Read and R. J. Wilson, An Atlas of Graphs, Oxford, 1998.
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).
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..87 (first 31 terms from David Wasserman)
R. K. Guy, The Second Strong Law of Small Numbers, Math. Mag, 63 (1990), no. 1, 3-20. [Annotated scanned copy]
F. Harary, The number of linear, directed, rooted, and connected graphs, Trans. Amer. Math. Soc. 78 (1955), 445-463.
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
Eric Weisstein's World of Mathematics, Disconnected Graph.
Eric Weisstein's World of Mathematics, k-Connected Graph.
Eric Weisstein's World of Mathematics, k-Edge-Connected Graph.
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MATHEMATICA
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<< "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}] (* Jean-François Alcover, Nov 24 2011 *)
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CROSSREFS
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Equals (A000088) minus (A001349).
Sequence in context: A212827 A212828 A212830 * A149875 A221546 A085632
Adjacent sequences: A000716 A000717 A000718 * A000720 A000721 A000722
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane
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EXTENSIONS
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More terms from Christian G. Bower
Further terms from Vladeta Jovovic, Apr 14 2000
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STATUS
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approved
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