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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 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 * A222472 A132847 A275620 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

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Last modified October 21 07:45 EDT 2021. Contains 348150 sequences. (Running on oeis4.)