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

1,3

Links

Table of n, a(n) for n=1..15.

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

Formula

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

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 *)

Crossrefs

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

Sequence in context: A006390 A100597 A352184 * A341360 A320954 A389488

Adjacent sequences: A022559 A022560 A022561 * A022563 A022564 A022565

Keyword

nonn,nice,more

Author

N. J. A. Sloane

Extensions

Corrected and extended by Gordon Royle, May 16 2003

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

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

Status

approved