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%I #18 Sep 18 2019 04:56:26
%S 1,1,2,6,16,49,129,481,1845,9506,57896,463909,4769436,65179170,
%T 1187099045,29082860878,960963147303,42920936851975,2594399793419459,
%U 212465886865393053,23596018831885668391,3557502387712889568013,728850489548729072323085
%N Number of unlabeled and connected graphs on n vertices which are either bipartite or co-bipartite.
%C G is bipartite iff the vertices can be partitioned into two sets such that all the edges in the graph go from one of these sets to the other. G is cobipartite iff the complement of G is bipartite.
%C For n >= 5, no graph can be both bipartite and co-bipartite. - _Falk Hüffner_, Jan 22 2016
%H Andrew Howroyd, <a href="/A079565/b079565.txt">Table of n, a(n) for n = 1..50</a>
%F For n >= 5, a(n) = A079571(n) + A005142(n). - _Falk Hüffner_, Jan 22 2016
%e Let G be a graph with 5 vertices, 4 of which form a path and the 5th adjacent only to the two vertices in the middle of the path. Then G is not bipartite nor cobipartite because there is a triangle in both G and its complement.
%t A005142 = Import["https://oeis.org/A005142/b005142.txt", "Table"][[All, 2]];
%t A033995 = Import["https://oeis.org/A033995/b033995.txt", "Table"][[All, 2]];
%t a[n_] := If[n<5, {1, 1, 2, 6}[[n]], A005142[[n+1]] + A033995[[n+1]] - Floor[n/2]];
%t a /@ Range[1, 50] (* _Jean-François Alcover_, Sep 17 2019 *)
%Y Cf. A005142, A079571.
%K nonn
%O 1,3
%A _Jim Nastos_, Jan 24 2003
%E More terms using formula by _Falk Hüffner_, Jan 22 2016
%E Terms a(21) and beyond from _Andrew Howroyd_, Sep 05 2018
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