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A077269 Number of connected squarefree graphs on n nodes. 5

%I

%S 1,1,2,3,8,19,57,186,740,3389,18502,120221,932260,8596844,93762704,

%T 1201732437,17992683043,313098431306,6305419392541

%N Number of connected squarefree graphs on n nodes.

%H Felix Arends, Joel Ouaknine, and Charles W. Wampler, <a href="https://arxiv.org/abs/1111.3301">On Searching for Small Kochen-Specker Vector Systems</a> (extended version), arXiv:1111.3301 [quant-ph], 2011.

%H CombOS - Combinatorial Object Server, <a href="http://combos.org/nauty">generate graphs</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Square-FreeGraph.html">Square-Free Graph</a>

%F Inverse Euler transform of A006786. - _Andrew Howroyd_, Nov 03 2017

%t A006786 = {1, 2, 4, 8, 18, 44, 117, 351, 1230, 5069, 25181, 152045, 1116403, 9899865, 104980369, 1318017549, 19427531763, 333964672216, 6660282066936};

%t mob[m_, n_] := If[Mod[m, n] == 0, MoebiusMu[m/n], 0];

%t EULERi[b_] := Module[{a, c, i, d}, c = {}; For[i = 1, i <= Length[b], i++, c = Append[c, i*b[[i]] - Sum[c[[d]]*b[[i - d]], {d, 1, i - 1}]]]; a = {}; For[i = 1, i <= Length[b], i++, a = Append[a, (1/i)*Sum[mob[i, d]*c[[d]], {d, 1, i}]]]; Return[a]];

%t EULERi[A006786] (* _Jean-Fran├žois Alcover_, Aug 18 2018, after _Andrew Howroyd_ *)

%Y Cf. A006786.

%K nonn,more

%O 1,3

%A _Eric W. Weisstein_, Nov 01 2002

%E More terms from _Jim Nastos_, Aug 27 2004

%E 4 more terms from _Vladeta Jovovic_, May 17 2008

%E a(18)-a(19) using _Brendan McKay_'s extension to A006786 by _Alois P. Heinz_, Mar 11 2018

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Last modified July 14 16:21 EDT 2020. Contains 335729 sequences. (Running on oeis4.)