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

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

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

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[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

Column 3 of A339428.

Cf. A000081.

Sequence in context: A207008 A077996 A330453 * A354645 A371956 A282732

Adjacent sequences: A029849 A029850 A029851 * A029853 A029854 A029855

Keyword

nonn

Author

Christian G. Bower

Status

approved