A079571 Number of unlabeled, connected graphs on n vertices whose complements are bipartite.

1, 1, 1, 2, 5, 11, 32, 85, 299, 1115, 5474, 32298, 251129, 2527706, 33985846, 611846933, 14864650916, 488222721984, 21712049275189, 1308300679611460, 106897965189674281, 11852113048215107812, 1784730721403509209204, 365323537513403184463262

Offset

0,4

Comments

Equivalently, number of bipartite graphs whose complement is connected. The only bipartite graphs with disconnected complement are complete bipartite graphs. - Falk Hüffner, Jan 22 2016

Links

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

Formula

a(n) = A033995(n) - floor(n/2).

Mathematica

A005142 = Import["https://oeis.org/A005142/b005142.txt", "Table"][[All, 2]];
etr[p_] := Module[{b}, b[n_] := b[n] = If[n == 0, 1, Sum[Sum[d*p[d], {d, Divisors[j]}]*b[n - j], {j, 1, n}]/n]; b];
b = etr[A005142[[# + 1]]&];
a[n_] := b[n] - Floor[n/2];
a /@ Range[0, 50] (* Jean-François Alcover, Sep 17 2019 *)

Crossrefs

Cf. A005142, A033995.

Sequence in context: A174537 A101837 A124483 * A151395 A056364 A205799

Adjacent sequences: A079568 A079569 A079570 * A079572 A079573 A079574

Keyword

nonn

Author

Jim Nastos, Jan 24 2003

Extensions

Corrected and extended using formula by Falk Hüffner, Jan 22 2016

a(0)=1 prepended and terms a(21) and beyond from Andrew Howroyd, Sep 05 2018

Status

approved