cp's OEIS Frontend

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

%I A022562 #33 Feb 16 2025 08:32:34
%S A022562 1,1,2,5,14,50,191,881,4494,26389,184749,1728404,23805256,491544474,
%T A022562 14491876320
%N A022562 Number of connected claw-free unlabeled graphs on n nodes.
%H A022562 R. Faudree, E. Flandrin and Z. Ryjacek, <a href="https://doi.org/10.1016/S0012-365X(96)00045-3">Claw-free graphs - a survey</a>, Discr. Math., 164 (1997), 87-147.
%H A022562 F. Hüffner, <a href="https://github.com/falk-hueffner/tinygraph">tinygraph</a>, software for generating integer sequences based on graph properties, version 8489dde.
%H A022562 Gordon Royle, <a href="http://www.csse.uwa.edu.au/~gordon/cf.zip">1728404 distinct 12-vertex connected clawfree graphs</a>
%H A022562 Gordon Royle, <a href="http://www.csse.uwa.edu.au/~gordon/g6.html">g6 format</a>
%H A022562 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Claw-FreeGraph.html">Claw-Free Graph</a>
%H A022562 Wikipedia, <a href="https://en.wikipedia.org/wiki/Claw-free_graph">Claw-free Graph</a>
%F A022562 Inverse Euler transform of A086991. - _Andrew Howroyd_, Nov 03 2017
%t A022562 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]}]];
%t A022562 A086991 = Cases[Import["https://oeis.org/A086991/b086991.txt", "Table"], {_, _}][[All, 2]];
%t A022562 EulerInvTransform[A086991] (* _Jean-François Alcover_, Aug 20 2019, code due to _Gus Wiseman_ *)
%Y A022562 Cf. A022563, A022564, A058929, A086991 (Euler transform).
%K A022562 nonn,nice,more
%O A022562 1,3
%A A022562 _N. J. A. Sloane_
%E A022562 Corrected and extended by _Gordon F. Royle_, May 16 2003
%E A022562 Term a(14) added by _Gordon F. Royle_, Aug 06 2008
%E A022562 Term a(15) added using tinygraph by _Falk Hüffner_, Jan 12 2016