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A058915 Number of graphs with 3 distinct components. 2
2, 7, 34, 181, 1266, 14106, 293756, 12362198, 1032671168, 166176421788, 50672459139597, 29105501987344357, 31455795559882541775, 64032588337815572241795, 246000022800939308314311897 (list; graph; refs; listen; history; text; internal format)
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..20.

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-Fran├žois Alcover in A001349 *)

CROSSREFS

Cf. A001349. Column 3 of A217955.

Sequence in context: A222940 A227120 A023053 * A273030 A020054 A206240

Adjacent sequences:  A058912 A058913 A058914 * A058916 A058917 A058918

KEYWORD

easy,nonn

AUTHOR

Vladeta Jovovic, Jan 11 2001

STATUS

approved

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Last modified November 13 11:09 EST 2018. Contains 317133 sequences. (Running on oeis4.)