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A029853 Number of connected functions on n points with a loop of length 4. 3
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
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
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[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
Column 4 of A339428.
Sequence in context: A034755 A297608 A034756 * A104500 A119716 A000626
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified June 17 21:09 EDT 2024. Contains 373464 sequences. (Running on oeis4.)