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A060171
Number of orbits of length n under a map whose periodic points seem to be counted by A006953.
11
12, 54, 80, 30, 24, 5400, 0, 990, 1568, 636, 24, 2720, 0, 240, 5704, 510, 0, 3835776, 0, 26724, 3600, 108, 24, 89760, 0, 240, 1064, 120, 24, 113569300, 0, 510, 11752, 0, 264, 278281640
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
KEYWORD
easy,nonn
AUTHOR
Thomas Ward, Mar 13 2001
STATUS
approved