OFFSET
1,2
COMMENTS
The sequence A000364 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
Alois P. Heinz, Table of n, a(n) for n = 1..243
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)*A000364(n/d).
EXAMPLE
u(3) = 20 since the conjectured map whose periodic points are counted by A000364 would have 1 fixed point and 61 points of period 3, so it must have 20 orbits of length 3.
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Thomas Ward, Mar 13 2001
STATUS
approved