A060166 Number of orbits of length n under the map whose periodic points are counted by A001641.

1, 1, 1, 2, 3, 4, 7, 10, 17, 26, 44, 68, 115, 184, 306, 500, 835, 1374, 2301, 3822, 6409, 10718, 18028, 30280, 51077, 86130, 145641, 246370, 417600, 708246, 1203069, 2045010, 3480408, 5927660, 10105819, 17241140, 29439580, 50302162, 86012630, 147166248, 251963055, 431633348

Offset

1,4

Comments

The sequence A001641 seems to record the number of points of period n under a map. The number of orbits of length n for this map gives the sequence above.

Links

Table of n, a(n) for n=1..42.

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 divides n } mu(d)*A001641(n/d).

Example

a(7) = 7 since a map whose periodic points are counted by A001641 would have 1 fixed point and 50 points of period 7, hence 7 orbits of length 7.

Prog

(PARI) a001641(n)=if(n<0, 0, polcoeff(x*(1+2*x+4*x^3)/(1-x-x^2-x^4)+x*O(x^n), n))
a(n) = sumdiv(n, d, moebius(d)*a001641(n/d))/n; \\ Michel Marcus, Sep 10 2017

Crossrefs

Cf. A001641, A060164, A060165, A060167, A060168, A060169, A060170, A060171, A060171.

Sequence in context: A082958 A218495 A166012 * A053634 A094863 A094862

Adjacent sequences: A060163 A060164 A060165 * A060167 A060168 A060169

Keyword

easy,nonn

Author

Thomas Ward, Mar 13 2001

Extensions

More terms from Michel Marcus, Sep 10 2017

Status

approved