A157016 -id:A157016 - cp's OEIS frontend

A157015 Number of graphs with n vertices having a bipartite connected component.

0, 1, 2, 3, 8, 18, 60, 232, 1389, 14174, 291396, 12307993, 1031244083, 166112993730, 50667178220215, 29104660317374991, 31455540471012663839, 64032442292149795841796, 245999865227419158171980939, 1787823661072649054474456291897, 24639596830978183991220162941946112

Offset: 0

Tanya Khovanova, Feb 21 2009

nonn

Andrew Howroyd, Table of n, a(n) for n = 0..50
Tanya Khovanova, Can Someone Be Straight? [From _Tanya Khovanova_, Sep 23 2009]

cbs[g_] := Or @@ Map[BipartiteQ, Map[InduceSubgraph[g, # ] &, ConnectedComponents[g]]] Table[Count[Map[cbs, ListGraphs[n]], True], {n, 7}]
(* from Eric W. Weisstein, May 02 2009: *) First do: <

a(n) = A000088(n) - A157016(n).

Incorrect comment deleted by N. J. A. Sloane, Feb 22 2009
Terms from a(8) onwards from Max Alekseyev, Feb 22 2009
Offset corrected by Max Alekseyev, Feb 24 2009
a(8) corrected by W. Edwin Clark, May 02 2009; confirmed by Eric W. Weisstein
Corrected by Max Alekseyev and Vladeta Jovovic, May 02 2009
a(18)-a(20) from Max Alekseyev, Jun 24 2013

A157051 Number of connected unlabeled non-bipartite graphs on n nodes.

Original entry on oeis.org

0, 0, 0, 1, 3, 16, 95, 809, 10935, 260350, 11712539, 1006674967, 164059617696, 50335905627489, 29003487431654737, 31397381142185989848, 63969560113210957966315, 245871831682083553779103249, 1787331725248899067681312999794, 24636021429399867654036551645873645, 645465483198722799426625560872826564232

Offset: 0

Max Alekseyev, Feb 22 2009

nonn

Inverse Euler transform of A157016.

Andrew Howroyd, Table of n, a(n) for n = 0..50

A001349 = Cases[Import["https://oeis.org/A001349/b001349.txt", "Table"], {, }][[All, 2]];
A005142 = Cases[Import["https://oeis.org/A005142/b005142.txt", "Table"], {, }][[All, 2]];
a[n_] := A001349[[n + 1]] - A005142[[n + 1]];
a /@ Range[0, 50] (* Jean-François Alcover, Sep 21 2019 *)

a(n) = A001349(n) - A005142(n).

a(0) corrected, a(18)-a(20) added by Max Alekseyev, Jun 24 2013

cp's OEIS Frontend

A157015 Number of graphs with n vertices having a bipartite connected component.

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