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A092239 Number of orbits of length n under the map whose periodic points are counted by A061693. 0
0, 2, 9, 42, 225, 1260, 7497, 46176, 293382, 1908150, 12655269, 85287870, 582628683, 4026368514, 28104231825, 197884340160, 1404038987577, 10029929788566, 72086075552493, 520920674929650 (list; graph; refs; listen; history; text; internal format)
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: A289684 A280955 A276508 * A222472 A132847 A275620

Adjacent sequences:  A092236 A092237 A092238 * A092240 A092241 A092242

KEYWORD

nonn,changed

AUTHOR

Thomas Ward, Feb 24 2004

EXTENSIONS

Name clarified by Michel Marcus, May 14 2015

STATUS

approved

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Last modified February 25 22:37 EST 2021. Contains 341618 sequences. (Running on oeis4.)