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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: 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

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Last modified September 19 13:29 EDT 2024. Contains 376012 sequences. (Running on oeis4.)