A091160 Number of orbits of length n under the map whose periodic points are counted by A061687.

1, 16, 2835, 2370752, 6611343125, 48887897438124, 821067869874486556, 28006755051982013513984, 1782755223314276717178818904, 198173677662343700104263938337400, 36467946245662764068249155883368682252, 10631160782054640951386529213624176084501136

Offset

1,2

Comments

Old name was: A061687 appears to count the periodic points for a certain map. If so, then this is the sequence of the numbers of orbits of length n for that map.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..100

Y. Puri and T. Ward, Arithmetic and growth of periodic orbits, J. Integer Seqs., Vol. 4 (2001), #01.2.1.

J.-M. Sixdeniers, K. A. Penson and A. I. Solomon, Extended Bell and Stirling Numbers From Hypergeometric Exponentiation, J. Integer Seqs. Vol. 4 (2001), #01.1.4.

Thomas Ward, Exactly realizable sequences. [local copy].

Formula

If b(n) is the (n+1)th term of A061687, then a(n) = (1/n)*Sum_{d|n} mu(d)*b(n/d).

Example

b(1)=1, b(3)=8506, so a(3) = (1/3)*(8506-1) = 2835.

Maple

with(numtheory):
b:= proc(n) option remember;
      `if`(n=0, 1, add(binomial(n, k)^6*(n-k)*b(k)/n, k=0..n-1))
    end:
a:= n-> add(mobius(d)*b(n/d), d=divisors(n))/n:
seq(a(n), n=1..15);  # Alois P. Heinz, Mar 19 2014

Mathematica

b[n_] := b[n] = If[n==0, 1, Sum[Binomial[n, k]^6 (n-k)b[k]/n, {k, 0, n-1}]];
a[n_] := Sum[MoebiusMu[d] b[n/d], {d, Divisors[n]}]/n;
Array[a, 15] (* Jean-François Alcover, Nov 18 2020, after Alois P. Heinz *)

Crossrefs

Cf. A061687.

Sequence in context: A016876 A221253 A123282 * A049030 A223068 A051551

Adjacent sequences: A091157 A091158 A091159 * A091161 A091162 A091163

Keyword

nonn

Author

Thomas Ward, Feb 24 2004

Extensions

More terms from Alois P. Heinz, Mar 19 2014

Name clarified by Michel Marcus, May 13 2015

Status

approved