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A060167 Number of orbits of length n under the map whose periodic points are counted by A001642. 9
1, 1, 1, 2, 4, 5, 9, 13, 23, 36, 63, 101, 175, 290, 497, 840, 1445, 2460, 4247, 7293, 12619, 21805, 37856, 65695, 114401, 199280, 347944, 607959, 1064130, 1864083, 3269948, 5740840, 10090148, 17748870, 31250297, 55063603, 97102485, 171355485, 302605780, 534729160, 945513850 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

The sequence A001642 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..41.

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)*A001642(n/d).

EXAMPLE

u(7) = 9 since a map whose periodic points are counted by A001642 would have 1 fixed point and 64 points of period 7, hence 9 orbits of length 7.

PROG

(PARI) a001642(n) = if(n<0, 0, polcoeff(x*(1+2*x+4*x^3+5*x^4)/(1-x-x^2-x^4-x^5)+x*O(x^n), n));

a(n) = (1/n)*sumdiv(n, d, moebius(d)*a001642(n/d)); \\ Michel Marcus, Sep 11 2017

CROSSREFS

Cf. A001642, A060164, A060165, A060166, A060168, A060169, A060170, A060171, A060171.

Sequence in context: A325716 A068372 A068370 * A234588 A118550 A126697

Adjacent sequences:  A060164 A060165 A060166 * A060168 A060169 A060170

KEYWORD

easy,nonn

AUTHOR

Thomas Ward, Mar 13 2001

EXTENSIONS

More terms from Michel Marcus, Sep 11 2017

STATUS

approved

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Last modified September 27 04:33 EDT 2022. Contains 357052 sequences. (Running on oeis4.)