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A029853 Number of connected functions on n points with a loop of length 4. 1
1, 1, 4, 11, 35, 97, 282, 792, 2243, 6275, 17602, 49206, 137713, 385208, 1078667, 3022342, 8478199, 23807190, 66932592, 188394855, 530911452, 1497892857, 4230987944, 11964356354, 33869704270, 95982410945, 272279600817, 773153124315, 2197492308752 (list; graph; refs; listen; history; text; internal format)
OFFSET

4,3

LINKS

Table of n, a(n) for n=4..32.

FORMULA

G.f.: A(x) = ( B(x)^4 + B(x^2)^2 + 2*B(x^4) )/4 where B(x) is the 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[4], s] /.

   Table[s[i] -> Sum[b[[k]] x^(k*i), {k, 1, nn}], {i, 1, 4}], {x, 0,

nn}], x] (* Geoffrey Critzer, Aug 08 2013 *)

CROSSREFS

Sequence in context: A034755 A297608 A034756 * A104500 A119716 A000626

Adjacent sequences:  A029850 A029851 A029852 * A029854 A029855 A029856

KEYWORD

nonn

AUTHOR

Christian G. Bower

STATUS

approved

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Last modified February 23 17:23 EST 2018. Contains 299584 sequences. (Running on oeis4.)