A058915 Number of graphs with 3 distinct components.

2, 7, 34, 181, 1266, 14106, 293756, 12362198, 1032671168, 166176421788, 50672459139597, 29105501987344357, 31455795559882541775, 64032588337815572241795, 246000022800939308314311897, 1787823981552130153705588238463, 24639598061620749532556334695267215

Offset

6,1

References

F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, page 48, (2.6.3).

Links

Table of n, a(n) for n=6..22.

Formula

G.f.: 1/6*(f(x)^3 - 3*f(x)*f(x^2) + 2*f(x^3)), where f(x) = g(x) - 1 and g(x) is g.f. for connected graphs. Cf. A001349.

Mathematica

Needs["Combinatorica`"]; max=25; A000088=Table[NumberOfGraphs[n], {n, 0, max}]; f[x_]=1-Product[1/(1-x^k)^a[k], {k, 1, max}]; a[0]=a[1]=a[2]=1; coes=CoefficientList[Series[f[x], {x, 0, max}], x]; sol=First[Solve[Thread[Rest[coes+A000088]== 0]]]; cg=Table[a[n], {n, 1, max}]/.sol; Take[CoefficientList[CycleIndex[AlternatingGroup[3], s]-CycleIndex[SymmetricGroup[3], s]/.Table[s[j]->Table[Sum[cg[[i]] x^(k*i), {i, 1, max}], {k, 1, max}][[j]], {j, 1, 3}], x], {7, max}] (* Geoffrey Critzer, Oct 15 2012; after code by Jean-François Alcover in A001349 *)

Crossrefs

Cf. A001349. Column 3 of A217955.

Sequence in context: A376055 A023053 A377963 * A273030 A020054 A206240

Adjacent sequences: A058912 A058913 A058914 * A058916 A058917 A058918

Keyword

easy,nonn

Author

Vladeta Jovovic, Jan 11 2001

Extensions

More terms from Sean A. Irvine, Sep 05 2022

Status

approved