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A001435 Number of connected graphs with n nodes and n+1 edges.
(Formerly M3889 N1597)
3
0, 0, 0, 1, 5, 19, 67, 236, 797, 2678, 8833, 28908, 93569, 300748, 959374, 3042808, 9597679, 30134509, 94218306, 293509092, 911325798, 2821327949, 8711297753, 26833501800, 82476837698, 253007383067, 774737986836 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,5
COMMENTS
This enumerates the connected graphs of complexity 2, in the terminology of Spencer, p. 720. We define the complexity of a component [of the random graph] with V vertices and E edges as E-V+1. Trees [A000055] and unicyclic graphs [A001429] have complexity 0 and 1, respectively, and are called simple. A diagonal of A076263. - Jonathan Vos Post, Jun 26 2010
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
Joel Spencer, The Giant Component: The Golden Anniversary, Notices of the AMS, Vol. 57, No. 6, June/July 2010, 720-724
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.
CROSSREFS
Sequence in context: A035344 A114277 A104496 * A359293 A092492 A070857
KEYWORD
nonn
AUTHOR
EXTENSIONS
Description corrected by and more terms from Ronald C. Read, Aug 02 1996
a(27) corrected by Sean A. Irvine, Jul 23 2012
STATUS
approved

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Last modified March 28 22:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)