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 A029852 Number of connected functions on n points with a loop of length 3. 3
 1, 1, 3, 9, 23, 62, 169, 451, 1217, 3291, 8916, 24243, 66155, 181053, 497134, 1369064, 3780942, 10469573, 29063361, 80867990, 225508124, 630145449, 1764240907, 4948365051, 13902893423, 39124094362, 110265280739, 311208414556, 879523722747, 2488832434859 (list; graph; refs; listen; history; text; internal format)
 OFFSET 3,3 LINKS Alois P. Heinz, Table of n, a(n) for n = 3..1000 FORMULA G.f.: A(x) = ( B(x)^3 + 2*B(x^3) )/3 where B(x) is o.g.f. for A000081. - Geoffrey Critzer, Aug 09 2013 a(n) ~ A187770 * A051491^n / n^(3/2). - Vaclav Kotesovec, Dec 25 2020 MATHEMATICA nn = 20; f[x_] := Sum[a[n] x^n, {n, 0, nn}]; sol = SolveAlways[   0 == Series[     f[x] - x Product[1/(1 - x^i)^a[i], {i, 1, nn}], {x, 0, nn}],   x]; b = Flatten[Table[a[n], {n, 1, nn}] /. sol]; CoefficientList[ Series[CycleIndex[CyclicGroup[3], s] /.    Table[s[i] -> Sum[b[[k]] x^(k*i), {k, 1, nn}], {i, 1, 3}], {x, 0, nn}], x] (* Geoffrey Critzer, Aug 08 2013 *) CROSSREFS Column 3 of A339428. Cf. A000081. Sequence in context: A207008 A077996 A330453 * A282732 A253244 A018044 Adjacent sequences:  A029849 A029850 A029851 * A029853 A029854 A029855 KEYWORD nonn AUTHOR STATUS approved

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Last modified June 18 20:04 EDT 2021. Contains 345121 sequences. (Running on oeis4.)