A022562 Number of connected claw-free unlabeled graphs on n nodes.

1, 1, 2, 5, 14, 50, 191, 881, 4494, 26389, 184749, 1728404, 23805256, 491544474, 14491876320

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• nice
• more

Links

• R. Faudree, E. Flandrin and Z. Ryjacek, Claw-free graphs - a survey, Discr. Math., 164 (1997), 87-147.
• F. Hüffner, tinygraph, software for generating integer sequences based on graph properties, version 8489dde.
• Gordon Royle, 1728404 distinct 12-vertex connected clawfree graphs
• Gordon Royle, g6 format
• Eric Weisstein's World of Mathematics, Claw-Free Graph
• Wikipedia, Claw-free Graph

Crossrefs

Cf. A022563, A022564, A058929, A086991 (Euler transform).

Programs

Mathematica

EulerInvTransform[seq_] := Module[{final = {}}, For[i = 1, i <= Length[seq], i++, AppendTo[final, i*seq[[i]] - Sum[final[[d]]*seq[[i - d]], {d, i - 1}]]]; Table[Sum[MoebiusMu[i/d]*final[[d]], {d, Divisors[i]}]/i, {i, Length[seq]}]];
A086991 = Cases[Import["https://oeis.org/A086991/b086991.txt", "Table"], {, }][[All, 2]];
EulerInvTransform[A086991] (* Jean-François Alcover, Aug 20 2019, code due to Gus Wiseman *)

Formula

Inverse Euler transform of A086991. - Andrew Howroyd, Nov 03 2017

Extensions

Corrected and extended by Gordon F. Royle, May 16 2003

Term a(14) added by Gordon F. Royle, Aug 06 2008

Term a(15) added using tinygraph by Falk Hüffner, Jan 12 2016