A132220 Number of line graphs on n unlabeled nodes.

1, 2, 4, 10, 24, 63, 166, 471, 1408, 4436, 14719, 51468, 188754, 725010, 2907576, 12141462, 52654529, 236584104, 1098926868, 5266708497, 25997964452, 131975740172, 688019138485, 3678898458587, 20153878941460, 113000861804642, 647866385202660, 3794917399892511, 22693153274994534, 138436809489370914, 860962282687080614

Offset: 1

Author

Vladeta Jovovic, Aug 14 2007

Keywords

• nonn

Links

• Max Alekseyev, Table of n, a(n) for n = 1..60
• Eric Weisstein's World of Mathematics, Line Graph.

Crossrefs

Euler transform of A003089.

Cf. A132219 (labeled case).

Cf. A000664.

Programs

Mathematica

<< Combinatorica`; With[{e = Table[NumberOfGraphs[2 n, n], {n, 12}]}, e - Join[{0, 0, 1}, Drop[e, -3]]] (* Eric W. Weisstein, Oct 30 2017 *)
<< Combinatorica`; With[{e = Table[Coefficient[GraphPolynomial[2 n, x], x, n], {n, 12}]}, e - Join[{0, 0, 1}, Drop[e, -3]]] (* Eric W. Weisstein, Oct 30 2017 *)

Formula

For n>=3, a(n) = A000664(n) - A000664(n-3). - Max Alekseyev, Sep 03 2016

Extensions

a(25)-a(60) from Max Alekseyev, Sep 07 2016