OFFSET
1,1
COMMENTS
The sequence A006953 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|n} mu(d)*A006953(n/d).
EXAMPLE
u(3) = 80 since a map whose periodic points are counted by A006953 has 12 fixed points and 252 points of period 3, hence 80 orbits of length 3.
PROG
(PARI) a(n) = sumdiv(n, d, moebius(d)*denominator(bernfrac(2*n/d)/(2*n/d)))/n; \\ Michel Marcus, Sep 10 2017
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Thomas Ward, Mar 13 2001
STATUS
approved