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A002905
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Number of connected graphs with n edges.
(Formerly M2486 N0985)
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14
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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; refs; listen; history; internal format)
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OFFSET
| 0,4
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REFERENCES
| G. A. Baker et al., High-temperature expansions for the spin-1/2 Heisenberg model, Phys. Rev., 164 (1967), 800-817.
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.
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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.
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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".
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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 * A087610 A191636 A156436
Adjacent sequences: A002902 A002903 A002904 * A002906 A002907 A002908
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KEYWORD
| nonn,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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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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