A077269 Number of connected squarefree graphs on n nodes.

1, 1, 2, 3, 8, 19, 57, 186, 740, 3389, 18502, 120221, 932260, 8596844, 93762704, 1201732437, 17992683043, 313098431306, 6305419392541

Offset: 1

Author

Eric W. Weisstein, Nov 01 2002

Keywords

• nonn
• more

Comments

From R. J. Mathar, Apr 04 2022 (Start)

The sequence contains the row sums of the number of connected squarefree graphs on V vertices with E edges, the triangle with V>=0, E>=0:

1 ;

1 ;

0 1;

0 0 1 1;

0 0 0 2 1;

0 0 0 0 3 4 1;

0 0 0 0 0 6 9 4;

0 0 0 0 0 0 11 24 17 5;

0 0 0 0 0 0 0 23 61 66 31 5;

0 0 0 0 0 0 0 0 47 169 248 192 74 10;

(End)

Links

• 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
• R. J. Mathar, Illustrations
• Eric Weisstein's World of Mathematics, Square-Free Graph
• Index entries for sequences of squarefree graphs

Crossrefs

Cf. A006786, A243243 (complement).

Programs

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-François Alcover, Aug 18 2018, after Andrew Howroyd *)

Formula

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

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