OFFSET
1,3
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
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]];
CROSSREFS
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
STATUS
approved