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A029852
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Number of connected functions on n points with a loop of length 3.
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3
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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
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OFFSET
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3,3
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 3..1000
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FORMULA
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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
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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[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 *)
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CROSSREFS
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Column 3 of A339428.
Cf. A000081.
Sequence in context: A207008 A077996 A330453 * A282732 A047085 A253244
Adjacent sequences: A029849 A029850 A029851 * A029853 A029854 A029855
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KEYWORD
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nonn
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AUTHOR
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Christian G. Bower
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STATUS
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approved
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