A086991 -id:A086991 - cp's OEIS frontend

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

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

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

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 *)

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

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

A352214 Largest number of maximal claw-free node-induced subgraphs of an n-node graph.

Original entry on oeis.org

1, 1, 1, 4, 7, 11, 23, 44, 71

Offset: 1

Pontus von Brömssen, Mar 08 2022

This sequence is log-superadditive, i.e., a(m+n) >= a(m)*a(n). By Fekete's subadditive lemma, it follows that the limit of a(n)^(1/n) exists and equals the supremum of a(n)^(1/n).

			All graphs with at most three nodes are claw-free, so a(n) = 1 for n <= 3 and any graph is optimal.
For 4 <= n <= 9, the following are all optimal graphs, i.e., graphs that have n nodes and a(n) maximal claw-free subgraphs:
  n = 4: K_{1,3};
  n = 5: K_{1,4};
  n = 6: K_{1,5}, K_{3,3} with one edge removed, and K_{3,3};
  n = 7: K_{3,4} with one edge removed;
  n = 8: K_{4,4} with one edge removed;
  n = 9: K_{4,5} with one edge removed.

Cf. A022562, A086991.

For a list of related sequences, see cross-references in A342211.

a(m+n) >= a(m)*a(n).

Limit_{n->oo} a(n)^(1/n) >= 71^(1/9) = 1.60581... .

cp's OEIS Frontend

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

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