A092239 Number of orbits of length n under the map whose periodic points are counted by A061693.

0, 2, 9, 42, 225, 1260, 7497, 46176, 293382, 1908150, 12655269, 85287870, 582628683, 4026368514, 28104231825, 197884340160, 1404038987577, 10029929788566, 72086075552493, 520920674929650

Offset

1,2

Comments

Old name was: A061693 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.

Links

Table of n, a(n) for n=1..20.

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-th term of A061693, then a(n) = (1/n)*Sum_{d|n}mu(d)a(n/d).

a(n) ~ 8^n / (Pi*sqrt(3)*n^2). - Vaclav Kotesovec, Sep 05 2019

Example

a(3)=9 since a(3)=(1/3)(b(3)-b(1)) where b is the sequence A061693, which starts 0,4,27.

Mathematica

Table[Sum[MoebiusMu[d] * (Sum[Binomial[n/d, k]^3, {k, 0, n/d}]/2 - 1), {d, Divisors[n]}]/n, {n, 1, 20}] (* Vaclav Kotesovec, Sep 05 2019 *)

Crossrefs

Cf. A061693.

Sequence in context: A280955 A276508 A347996 * A351881 A222472 A351882

Adjacent sequences: A092236 A092237 A092238 * A092240 A092241 A092242

Keyword

nonn

Author

Thomas Ward, Feb 24 2004

Extensions

Name clarified by Michel Marcus, May 14 2015

Status

approved