A126750 - OEIS

%I #21 May 31 2018 05:11:10

%S 0,0,0,1,1,5,8,42,146,956,6643,65921,818448,13442572,287665498,

%T 8099980771,300760170216,14791653463768,967055338887805,

%U 84368806391412395,9855854129239183783,1546801291978378704267

%N Number of 2-connected (or biconnected) graphs on n nodes with chromatic number 2.

%C Equally, number of 2-connected (or biconnected) bipartite graphs on n nodes.

%C Also number of biconnected triangle-free graphs on n nodes with chromatic number 2, since chromatic number 2 implies triangle-free. - _Gordon Royle_, Apr 11 2007

%C See the Gainer-Dewar/Gessel reference for formulas and Sage code. - _Ralf Stephan_, May 18 2013

%H Keith M. Briggs, <a href="http://keithbriggs.info/cgt.html">Combinatorial Graph Theory</a>

%H C. J. Colbourn and C. Huybrechts, <a href="https://doi.org/10.1016/j.disc.2007.09.039">Fully gated graphs,: recognition and convex operations</a>, Discrete Math., 308 (2008), 5184-5195.

%H A. Gainer-Dewar and I. M. Gessel, <a href="https://arxiv.org/abs/1304.0139">Enumeration of bipartite graphs and bipartite blocks</a>, arXiv:1304.0139 [math.CO], 2013-2014.

%Y A diagonal of triangle in A126749.

%K nonn

%O 1,6

%A _N. J. A. Sloane_, Feb 18 2007, Oct 01 2008