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A000664
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Number of graphs with n edges.
(Formerly M1400 N0545)
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70
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1, 1, 2, 5, 11, 26, 68, 177, 497, 1476, 4613, 15216, 52944, 193367, 740226, 2960520, 12334829, 53394755, 239544624, 1111261697, 5320103252, 26237509076, 133087001869, 693339241737, 3705135967663, 20286965943329, 113694201046379, 651571521170323, 3815204365835840, 22806847476040913, 139088381010541237, 864777487052916454
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,3
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COMMENTS
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These are simple graphs, unlabeled, with no isolated nodes, but are not necessarily connected.
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REFERENCES
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W. Oberschelp, Kombinatorische Anzahlbestimmungen in Relationen, Math. Ann., 174 (1967), 53-78.
J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 146.
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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Max Alekseyev, Table of n, a(n) for n = 0..60
Nicolas Borie, The Hopf Algebra of graph invariants, arXiv preprint arXiv:1511.05843, 2015
P. J. Cameron, Sequences realized by oligomorphic permutation groups, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.
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
Peter Steinbach, Field Guide to Simple Graphs, Volume 4, Overview of the 11 Parts (For Volumes 1, 2, 3, 4 of this book see A000088, A008406, A000055, A000664, respectively.)
Peter Steinbach, Field Guide to Simple Graphs, Volume 4, Part 1
Peter Steinbach, Field Guide to Simple Graphs, Volume 4, Part 2
Peter Steinbach, Field Guide to Simple Graphs, Volume 4, Part 3
Peter Steinbach, Field Guide to Simple Graphs, Volume 4, Part 4
Peter Steinbach, Field Guide to Simple Graphs, Volume 4, Part 5
Peter Steinbach, Field Guide to Simple Graphs, Volume 4, Part 6
Peter Steinbach, Field Guide to Simple Graphs, Volume 4, Part 7
Peter Steinbach, Field Guide to Simple Graphs, Volume 4, Part 8
Peter Steinbach, Field Guide to Simple Graphs, Volume 4, Part 9
Peter Steinbach, Field Guide to Simple Graphs, Volume 4, Part 10
Peter Steinbach, Field Guide to Simple Graphs, Volume 4, Part 11
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FORMULA
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a(n) = A008406(2*n,n). - Max Alekseyev, Sep 13 2016
Euler transform of A002905 (ignoring A002905(0)). - Franklin T. Adams-Watters Jul 03 2009
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EXAMPLE
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n=1: o-o (1)
n=2: o-o o-o, o-o-o (2)
n=3: o-o o-o o-o, o-o-o o-o, o-o-o-o, Y, triangle (5)
n=4: o-o o-o o-o o-o, o-o-o o-o o-o, o-o-o o-o-o, o-o o-o-o-o, o-o Y, o-o triangle,
o-o-o-o-o, >o-o-o, ><, square, triangle with tail (11)
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MATHEMATICA
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<< Combinatorica`; Table[NumberOfGraphs[2 n, n], {n, 0, 10}] (* Eric W. Weisstein, Oct 30 2017 *)
<< Combinatorica`; Table[Coefficient[GraphPolynomial[2 n, x], x, n], {n, 0, 10}] (* Eric W. Weisstein, Oct 30 2017 *)
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CROSSREFS
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Cf. A002905, A008406, A053418.
Row sums of A275421.
Cf. also A000088, A000055.
Sequence in context: A095892 A239311 A319760 * A242766 A182580 A067922
Adjacent sequences: A000661 A000662 A000663 * A000665 A000666 A000667
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KEYWORD
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nonn,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 Vladeta Jovovic, Jan 08 2000, Aug 14 2007
Edited by N. J. A. Sloane, Feb 26 2008
Example for n=2 corrected by Adrian Falcone (falcone(AT)gmail.com), Jan 28 2009
Zero term inserted by Franklin T. Adams-Watters, Jul 03 2009
a(25)-a(26) from Max Alekseyev, Sep 19 2009
a(27)-a(60) from Max Alekseyev, Sep 07 2016
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STATUS
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approved
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