OFFSET
1,4
COMMENTS
The sequence A001641 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)*A001641(n/d).
EXAMPLE
a(7) = 7 since a map whose periodic points are counted by A001641 would have 1 fixed point and 50 points of period 7, hence 7 orbits of length 7.
PROG
(PARI) a001641(n)=if(n<0, 0, polcoeff(x*(1+2*x+4*x^3)/(1-x-x^2-x^4)+x*O(x^n), n))
a(n) = sumdiv(n, d, moebius(d)*a001641(n/d))/n; \\ Michel Marcus, Sep 10 2017
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Thomas Ward, Mar 13 2001
EXTENSIONS
More terms from Michel Marcus, Sep 10 2017
STATUS
approved