[seqfan] Need help with graph sequences

[Tanya Khovanova]

Hello SeqFans,

I just submitted two sequences below. My inefficient program counts only the first 6 terms. The problem is that the second sequence exists in the OEIS, but I do not have any good reasons to believe that it is the same as mine, I need the next term to make sure. Can you do that?

%S A157015 1,2,3,8,18,60
%N A157015 Number of graphs with n vertices, such that a bipartite connected component exists. 
%C A157015 There exists a vertex which doesn't belong to a cycle of odd length. 


%S A157016 0,0,1,3,16,96
%N A157016 Number of graphs with n vertices such that a bipartite connected component doesn't exist. 
%C A157016 Any vertex is connected to a cycle of odd length. 
%t A157016 cbs[g_] := Or @@ Map[BipartiteQ, Map[InduceSubgraph[g, #] &, ConnectedComponents[g]]] Table[Count[Map[cbs, ListGraphs[n]], False], {n, 6}] 

Thank you in advance,
Tanya