A054960 Number of unlabeled graphs with n nodes and an odd number of edges.

0, 1, 2, 5, 16, 78, 522, 6168, 137316, 6002584, 509498932, 82545585936, 25251015681176, 14527077828617744, 15713242984902154384, 32000507852263778595584, 122967932076766466336249888, 893788862572805850273939095424, 12318904626562502262191503745716384

Offset: 1

Author

N. J. A. Sloane, May 24 2000

Keywords

• nonn
• easy

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..50
• V. A. Liskovets, Some easily derivable sequences, J. Integer Sequences, 3 (2000), #00.2.2.

Crossrefs

Cf. A000088, A000171.

Cf. A007869 for graphs with an even number of edges.

Programs

Mathematica

Table[Total[Table[NumberOfGraphs[n,m],{m,1,Binomial[n,2],2}]],{n,1,15}]  (* Geoffrey Critzer, Oct 20 2012 *)

Formula

a(n) = (A000088(n) - A000171(n))/2.

Extensions

More terms from Vladeta Jovovic, Jul 19 2000

Terms a(18) and beyond from Andrew Howroyd, Sep 17 2018