

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
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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 nth term of A061693, then a(n) = (1/n)*Sum_{dn}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



