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A077269 Number of connected squarefree graphs on n nodes. 5
1, 1, 2, 3, 8, 19, 57, 186, 740, 3389, 18502, 120221, 932260, 8596844, 93762704, 1201732437, 17992683043, 313098431306, 6305419392541 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..19.

Felix Arends, Joel Ouaknine, and Charles W. Wampler, On Searching for Small Kochen-Specker Vector Systems (extended version), arXiv:1111.3301 [quant-ph], 2011.

CombOS - Combinatorial Object Server, generate graphs

Eric Weisstein's World of Mathematics, Square-Free Graph

FORMULA

Inverse Euler transform of A006786. - Andrew Howroyd, Nov 03 2017

MATHEMATICA

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

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

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]];

EULERi[A006786] (* Jean-Fran├žois Alcover, Aug 18 2018, after Andrew Howroyd *)

CROSSREFS

Cf. A006786.

Sequence in context: A148040 A148041 A148042 * A294431 A148043 A321255

Adjacent sequences:  A077266 A077267 A077268 * A077270 A077271 A077272

KEYWORD

nonn,more

AUTHOR

Eric W. Weisstein, Nov 01 2002

EXTENSIONS

More terms from Jim Nastos, Aug 27 2004

4 more terms from Vladeta Jovovic, May 17 2008

a(18)-a(19) using Brendan McKay's extension to A006786 by Alois P. Heinz, Mar 11 2018

STATUS

approved

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Last modified September 24 17:09 EDT 2020. Contains 337321 sequences. (Running on oeis4.)