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A029853
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Number of connected functions on n points with a loop of length 4.
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3
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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
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OFFSET
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4,3
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LINKS
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FORMULA
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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
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MATHEMATICA
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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,
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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