A060170 Number of orbits of length n under the map whose periodic points are counted by A005809.

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

Offset: 1

Author

Thomas Ward, Mar 13 2001

Keywords

• easy
• nonn

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).

Examples

			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.
		

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.

Crossrefs

Cf. A005809, A060164, A060165, A060166, A060167, A060168, A060179, A060171, A060171, A060172, A060173.

Programs

PARI

a(n) = sumdiv(n, d, moebius(n/d)*binomial(3*d, d))/n; \\ Michel Marcus, Sep 10 2017

Formula

a(n) = (1/n)* Sum_{d|n} A008683(n/d)*A005809(d).

Extensions

Edited by Max Alekseyev, Feb 09 2016