

A002905


Number of connected graphs with n edges.
(Formerly M2486 N0985)


21



1, 1, 1, 3, 5, 12, 30, 79, 227, 710, 2322, 8071, 29503, 112822, 450141, 1867871, 8037472, 35787667, 164551477, 779945969, 3804967442, 19079312775, 98211456209, 518397621443, 2802993986619, 15510781288250, 87765472487659, 507395402140211, 2994893000122118, 18035546081743772, 110741792670074054, 692894304050453139
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OFFSET

0,4


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).


LINKS

Max Alekseyev, Table of n, a(n) for n = 0..60
G. A. Baker et al., Hightemperature expansions for the spin1/2 Heisenberg model, Phys. Rev., 164 (1967), 800817.
Nicolas Borie, The Hopf Algebra of graph invariants, arXiv preprint arXiv:1511.05843 [math.CO], 2015.
P. J. Cameron, Sequences realized by oligomorphic permutation groups, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.
Anjan Dutta, Hichem Sahbi, Graph Kernels based on High Order Graphlet Parsing and Hashing, arXiv:1803.00425 [cs.CV], 2018.
Gordon Royle, Small graphs
M. L. Stein and P. R. Stein, Enumeration of Linear Graphs and Connected Linear Graphs up to p = 18 Points. Report LA3775, Los Alamos Scientific Laboratory of the University of California, Los Alamos, NM, Oct 1967
Peter Steinbach, Field Guide to Simple Graphs, Volume 4, Part 1 (For Volumes 1, 2, 3, 4 of this book see A000088, A008406, A000055, A000664, respectively.)
Eric Weisstein's World of Mathematics, Polynema.


FORMULA

A000664 and this sequence are an Euler transform pair.  N. J. A. Sloane, Aug 30 2016


EXAMPLE

a(3) = 3 since the three connected graphs with three edges are a path, a triangle and a "Y".
The first difference between this sequence and A046091 is for n=9 edges where we see K_{3,3}, the wellknown "utility graph".


MATHEMATICA

terms = 61;
A000664 = DeleteCases[Import["https://oeis.org/A000664/b000664.txt", "Table"], {}][[2 ;; terms, 2]];
mob[m_, n_] := If[Mod[m, n] == 0, MoebiusMu[m/n], 0];
EULERi[b_List] := Module[{a, c, i, d}, c = {}; For[i = 1, i <= Length[b], i++, c = Append[c, i*b[[i]]  Sum[c[[d]]*b[[i  d]], {d, 1, i  1}]]]; a = {}; For[i = 1, i <= Length[b], i++, a = Append[a, Sum[mob[i, d]*c[[d]], {d, 1, i}]/i]]; Return[a]];
Join[{1}, EULERi[A000664]] {* JeanFrançois Alcover, May 10 2019 *)


CROSSREFS

Column sums of A054924 or equivalently row sums of A054923.
Cf. A000664, A046091 (for connected planar graphs).
Apart from a(3), same as A003089.
Sequence in context: A066951 A295065 A046091 * A220832 A323270 A087610
Adjacent sequences: A002902 A002903 A002904 * A002906 A002907 A002908


KEYWORD

nonn,nice,changed


AUTHOR

N. J. A. Sloane.


EXTENSIONS

More terms from Vladeta Jovovic, Jan 12 2000
More terms from Gordon F. Royle, Jun 05 2003
a(25)a(26) from Max Alekseyev, Sep 19 2009
a(27)a(60) from Max Alekseyev, Sep 07 2016


STATUS

approved



