

A015135


Consider Fibonaccitype sequences f(0)=X, f(1)=Y, f(k)=f(k1)+f(k2) mod n; all are periodic; sequence gives number of distinct periods.


1



1, 2, 2, 3, 3, 4, 2, 4, 3, 6, 3, 5, 2, 4, 5, 5, 2, 4, 3, 7, 3, 6, 2, 6, 4, 4, 4, 5, 3, 10, 3, 6, 5, 3, 5, 5, 2, 4, 4, 7, 2, 6, 2, 7, 7, 3, 2, 6, 3, 8, 4, 5, 2, 5, 5, 6, 5, 6, 3, 11, 2, 4, 5, 7, 5, 10, 2, 4, 3, 10, 3, 6, 2, 4, 7, 5, 5, 8, 3, 9, 5, 4, 2, 7, 5, 4, 5, 9, 2, 10, 4, 4, 5, 4, 7, 7, 2, 6, 7, 9, 3, 6, 2
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OFFSET

1,2


COMMENTS

Consider the 2step recursion f(k)=f(k1)+f(k2) mod n. For any of the n^2 initial conditions f(1) and f(2) in Zn, the recursion has a finite period. Each of these n^2 vectors belongs to exactly one orbit. In general, there are only a few different orbit lengths for each n. For n=8, there are 4 different lengths: 1, 3, 6 and 12. The maximum possible length of an orbit is A001175(n), the period of the Fibonacci 2step sequence mod n.  T. D. Noe, May 02 2005


LINKS



CROSSREFS

Cf. A015134 (orbits of 2step sequences), A106306 (primes that yield a simple orbit structure in 2step recursions).


KEYWORD

nonn


AUTHOR



EXTENSIONS

More terms from Larry Reeves (larryr(AT)acm.org), Jan 06 2005


STATUS

approved



