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 A060170 Number of orbits of length n under the map whose periodic points are counted by A005809. 12
 3, 6, 27, 120, 600, 3078, 16611, 91872, 520749, 3004200, 17594247, 104304888, 624801957, 3775722342, 22991161500, 140928011136, 868886416866, 5384796881850, 33525472069563, 209592223788000, 1315211209630794, 8281053081282894, 52301607644921259, 331260902534858976, 2103541885645955625, 13389670112374830378 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The sequence A005809 records the number of points of period n under a map. The number of orbits of length n for this map gives the sequence above. a(n) is divisible by n (cf. A268617), 2*a(n) is divisible by n^2 (cf. A268618). LINKS Table of n, a(n) for n=1..26. Y. Puri and T. Ward, Arithmetic and growth of periodic orbits, J. Integer Seqs., Vol. 4 (2001), #01.2.1. Yash Puri and Thomas Ward, A dynamical property unique to the Lucas sequence, Fibonacci Quarterly, Volume 39, Number 5 (November 2001), pp. 398-402. FORMULA a(n) = (1/n)* Sum_{d|n} A008683(n/d)*A005809(d). EXAMPLE a(3) = 27 since a map whose periodic points are counted by A005809 has 3 fixed points and 84 points of period 3, hence 27 orbits of length 3. PROG (PARI) a(n) = sumdiv(n, d, moebius(n/d)*binomial(3*d, d))/n; \\ Michel Marcus, Sep 10 2017 CROSSREFS Cf. A005809, A060164, A060165, A060166, A060167, A060168, A060179, A060171, A060171, A060172, A060173. Sequence in context: A215400 A215394 A222625 * A223143 A372039 A270889 Adjacent sequences: A060167 A060168 A060169 * A060171 A060172 A060173 KEYWORD easy,nonn AUTHOR Thomas Ward, Mar 13 2001 EXTENSIONS Edited by Max Alekseyev, Feb 09 2016 STATUS approved

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Last modified April 18 22:18 EDT 2024. Contains 371782 sequences. (Running on oeis4.)