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%I M3889 N1597 #35 Feb 16 2023 09:54:57
%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. - _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.
%K nonn
%O 1,5
%A _N. J. A. Sloane_
%E Description corrected by and more terms from Ronald C. Read, Aug 02 1996
%E a(27) corrected by _Sean A. Irvine_, Jul 23 2012
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