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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
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
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
KEYWORD
easy,nonn
AUTHOR
Thomas Ward, Mar 13 2001
EXTENSIONS
More terms from Michel Marcus, Sep 11 2017
STATUS
approved