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%I #19 Sep 06 2018 04:45:22
%S 0,1,2,3,8,18,60,232,1389,14174,291396,12307993,1031244083,
%T 166112993730,50667178220215,29104660317374991,31455540471012663839,
%U 64032442292149795841796,245999865227419158171980939,1787823661072649054474456291897,24639596830978183991220162941946112
%N Number of graphs with n vertices having a bipartite connected component.
%H Andrew Howroyd, <a href="/A157015/b157015.txt">Table of n, a(n) for n = 0..50</a>
%H Tanya Khovanova, <a href="http://blog.tanyakhovanova.com/?p=109">Can Someone Be Straight?</a> [From _Tanya Khovanova_, Sep 23 2009]
%F a(n) = A000088(n) - A157016(n).
%t cbs[g_] := Or @@ Map[BipartiteQ, Map[InduceSubgraph[g, # ] &, ConnectedComponents[g]]] Table[Count[Map[cbs, ListGraphs[n]], True], {n, 7}]
%t (* from _Eric W. Weisstein_, May 02 2009: *) First do: <<Combinatorica
%t In[2]:= Table[Count[Graphs[n], _?(Function[g,
%t Or @@ BipartiteQ /@ (InduceSubgraph[g, # ] & /@
%t ConnectedComponents[g])])], {n, 8}] // Timing
%K nonn
%O 0,3
%A _Tanya Khovanova_, Feb 21 2009
%E Incorrect comment deleted by _N. J. A. Sloane_, Feb 22 2009
%E Terms from a(8) onwards from _Max Alekseyev_, Feb 22 2009
%E Offset corrected by _Max Alekseyev_, Feb 24 2009
%E a(8) corrected by _W. Edwin Clark_, May 02 2009; confirmed by _Eric W. Weisstein_
%E Corrected by _Max Alekseyev_ and _Vladeta Jovovic_, May 02 2009
%E a(18)-a(20) from _Max Alekseyev_, Jun 24 2013
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