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A002905 Number of connected graphs with n edges.
(Formerly M2486 N0985)
+0
12
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 (list; graph; listen)
OFFSET

0,4

REFERENCES

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).

G. A. Baker et al., High-temperature expansions for the spin-1/2 Heisenberg model, Phys. Rev., 164 (1967), 800-817.

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.

LINKS

P. J. Cameron, Sequences realized by oligomorphic permutation groups, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.

Gordon Royle, Small graphs

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

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 well-known "utility graph".

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: A056690 A066951 A046091 this_sequence A087610 A156436 A099791

Adjacent sequences: A002902 A002903 A002904 this_sequence A002906 A002907 A002908

KEYWORD

nonn,nice

AUTHOR

N. J. A. Sloane (njas(AT)research.att.com).

EXTENSIONS

More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 12 2000

More terms from Gordon Royle (gordon(AT)maths.uwa.edu.au), Jun 05 2003

a(25)-a(26) from Max Alekseyev (maxale(AT)gmail.com), Sep 19 2009

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Last modified December 2 11:54 EST 2009. Contains 167921 sequences.


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