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A077269
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Number of connected squarefree graphs on n nodes.
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11
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1, 1, 2, 3, 8, 19, 57, 186, 740, 3389, 18502, 120221, 932260, 8596844, 93762704, 1201732437, 17992683043, 313098431306, 6305419392541
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OFFSET
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1,3
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COMMENTS
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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;
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LINKS
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FORMULA
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MATHEMATICA
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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]];
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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