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A029852 Number of connected functions on n points with a loop of length 3. 2
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

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

Cf. A000081.

Sequence in context: A061647 A207008 A077996 * A282732 A047085 A253244

Adjacent sequences:  A029849 A029850 A029851 * A029853 A029854 A029855

KEYWORD

nonn

AUTHOR

Christian G. Bower

STATUS

approved

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Last modified February 22 13:09 EST 2018. Contains 299454 sequences. (Running on oeis4.)