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 A274934 Number of unlabeled graphs with n nodes that have two components, neither of which is the empty graph. 10
 0, 0, 1, 1, 3, 8, 30, 145, 1028, 12320, 274806, 12007355, 1019030239, 165091859656, 50502058492266, 29054157815353374, 31426486309136279775, 64001015806929213894372, 245935864212056913811759534, 1787577725208700551275529005084 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..75 R. J. Mathar, Statistics on Small Graphs, arXiv:1709.09000 [math.CO] (2017) Table 81. FORMULA G.f.: [A(x)^2 + A(x^2)]/2 where A(x) is the o.g.f. for A001349 without the initial constant 1. a(n) = A201922(n,2). - R. J. Mathar, Jul 20 2016 EXAMPLE a(6) = A216785(6)+2 =30 where the two additional graphs have two equal components (of which there are A001349(3)=2 choices). MATHEMATICA terms = 20; 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]]; permcount[v_] := Module[{m = 1, s = 0, k = 0, t}, For[i = 1, i <= Length[v], i++, t = v[[i]]; k = If[i > 1 && t == v[[i - 1]], k + 1, 1]; m *= t*k; s += t]; s!/m]; edges[v_] := Sum[GCD[v[[i]], v[[j]]], {i, 2, Length[v]}, {j, 1, i - 1}] + Total[Quotient[v, 2]]; a88[n_] := Module[{s = 0}, Do[s += permcount[p]*2^edges[p], {p, IntegerPartitions[n]}]; s/n!]; A[x_] = Join[{1}, EULERi[Array[a88, terms]]].x^Range[0, terms] - 1; CoefficientList[(A[x]^2 + A[x^2])/2 + O[x]^terms, x] (* Jean-François Alcover, Sep 28 2018, after Andrew Howroyd in A001349 *) CROSSREFS Cf. A001349, A216785 (non-isomorphic components), A275165, A275166, column 2 of A201922. Sequence in context: A059171 A261766 A078619 * A066304 A298456 A145776 Adjacent sequences: A274931 A274932 A274933 * A274935 A274936 A274937 KEYWORD nonn AUTHOR R. J. Mathar and N. J. A. Sloane, Jul 18 2016 STATUS approved

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Last modified March 2 14:01 EST 2024. Contains 370485 sequences. (Running on oeis4.)