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

%I M3889 N1597

%S 0,0,0,1,5,19,67,236,797,2678,8833,28908,93569,300748,959374,3042808,

%T 9597679,30134509,94218306,293509092,911325798,2821327949,8711297753,

%U 26833501800,82476837698,253007383067,774737986836

%N Number of connected graphs with n nodes and n+1 edges.

%C 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. [From _Jonathan Vos Post_, Jun 26 2010]

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Sean A. Irvine, <a href="/A001435/b001435.txt">Table of n, a(n) for n = 1..40</a>

%H Joel Spencer, <a href="http://www.ams.org/notices/201006/rtx100600720p.pdf">The Giant Component: The Golden Anniversary</a>, Notices of the AMS, Vol. 57, No. 6, June/July 2010, 720-724

%H M. L. Stein and P. R. Stein, <a href="http://dx.doi.org/10.2172/4180737">Enumeration of Linear Graphs and Connected Linear Graphs up to p = 18 Points</a>. Report LA-3775, Los Alamos Scientific Laboratory of the University of California, Los Alamos, NM, Oct 1967.

%Y Cf. A000055, A001429, A076263. [_Jonathan Vos Post_, Jun 26 2010]

%K nonn

%O 1,5

%A _N. J. A. Sloane_.

%E Description corrected by and more terms from Ron Read (rcread(AT)math.uwaterloo.ca), Aug 02 1996

%E a(27) corrected by _Sean A. Irvine_, Jul 23 2012

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Last modified July 11 07:06 EDT 2020. Contains 335609 sequences. (Running on oeis4.)