A157016 Number of graphs with n vertices such that a bipartite connected component doesn't exist.

1, 0, 0, 1, 3, 16, 96, 812, 10957, 260494, 11713772, 1006689871, 164059928509, 50335918374222, 29003488479015273, 31397381309486933777, 63969560164056545231089, 245871831711240782887877980, 1787331725280384281389706209909, 24636021429463931875328533035140871, 645465483198968863672173418327800803328

Offset: 0

Author

Tanya Khovanova, Feb 21 2009

Keywords

• nonn

Links

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

Crossrefs

Cf. A000088, A157015, A157051.

Programs

Mathematica

cbs[g_] := Or @@ Map[BipartiteQ, Map[InduceSubgraph[g, # ] &, ConnectedComponents[g]]] Table[Count[Map[cbs, ListGraphs[n]], False], {n, 6}]
Table[Count[Map[cbs, ListGraphs[n]], False], {n,7}] (* Wouter Meeussen, Feb 21 2009 *)

Formula

Euler transform of A157051. - Max Alekseyev, Feb 22 2009

A157015(n) + a(n) = A000088(n).

Extensions

a(7) from Wouter Meeussen, Feb 21 2009

Formula and terms a(8)-a(17) from Max Alekseyev, Feb 22 2009

Corrected by Max Alekseyev and Vladeta Jovovic, May 02 2009

a(18)-a(20) from Max Alekseyev, Jun 24 2013