A001435 Number of connected graphs with n nodes and n+1 edges. (Formerly M3889 N1597)

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

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

Sean A. Irvine, Table of n, a(n) for n = 1..40

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

Cf. A000055, A001429, A076263.

Sequence in context: A035344 A114277 A104496 * A359293 A092492 A070857

Adjacent sequences: A001432 A001433 A001434 * A001436 A001437 A001438

Keyword

nonn

Author

N. J. A. Sloane

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