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%I M2501 #53 Feb 20 2023 22:08:38
%S 1,1,1,1,3,5,17,44,182,730,4032,25598,212780,2241730,31193324,
%T 575252112,14218209962,472740425319,21208887576786,1286099113807999,
%U 105567921675718772,11743905783670560579,1772771666309380358809,363526952035325887859823,101386021137641794979558045
%N Number of connected bipartite graphs with n nodes.
%C Also, the number of unlabeled connected bicolored graphs having n nodes; the color classes may be interchanged. - _Robert W. Robinson_
%C Also, for n>1, number of connected triangle-free graphs on n nodes with chromatic number 2. - Keith M. Briggs, Mar 21 2006 (cf. A116079).
%C Also, first diagonal of triangle in A126736.
%C EULER transform of [1, 1, 1, 3, 5, 17, ...] is A033995 [1, 2, 3, 7, 13, ...]. - _Michael Somos_, May 13 2019
%D R. C. Read and R. J. Wilson, An Atlas of Graphs, Oxford, 1998.
%D R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1976.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Andrew Howroyd, <a href="/A005142/b005142.txt">Table of n, a(n) for n = 0..50</a>
%H Jean-François Alcover, <a href="/A005142/a005142.txt">Mathematica program</a>
%H Keith M. Briggs, <a href="http://keithbriggs.info/cgt.html">Combinatorial Graph Theory</a>
%H CombOS - Combinatorial Object Server, <a href="http://combos.org/nauty">Generate graphs</a>
%H P. Hanlon, <a href="http://dx.doi.org/10.1016/0012-365X(79)90184-5">The enumeration of bipartite graphs</a>, Discrete Math. 28 (1979), 49-57.
%H Peter Steinbach, <a href="/A000088/a000088_17.pdf">Field Guide to Simple Graphs, Volume 1</a>, Part 17 (For Volumes 1, 2, 3, 4 of this book see A000088, A008406, A000055, A000664, respectively.)
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/BipartiteGraph.html">Bipartite Graph.</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/n-ChromaticGraph.html">n-Chromatic Graph</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/n-ColorableGraph.html">n-Colorable Graph</a>
%H Jonathan Wurtz and Danylo Lykov, <a href="https://arxiv.org/abs/2107.00677">The fixed angle conjecture for QAOA on regular MaxCut graphs</a>, arXiv:2107.00677 [quant-ph], 2021.
%F a(2*n+1) = A318870(2*n+1)/2, a(2*n) = (a(n) + A318869(n) + A318870(2*n) - A318870(n))/2. - _Andrew Howroyd_, Sep 04 2018
%t (* See the links section. *)
%Y Cf. A033995, A116079, A318869, A318870.
%K nonn,nice
%O 0,5
%A _N. J. A. Sloane_
%E More terms from Ronald C. Read.
%E a(0)=1 prepended by _Max Alekseyev_, Jun 24 2013
%E Terms a(21) and beyond from _Andrew Howroyd_, Sep 04 2018
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