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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
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
Sequence in context: A215400 A215394 A222625 * A223143 A372039 A270889
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.)