

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 period lengths.


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

Table of n, a(n) for n=1..103.
B. Avila and T. Khovanova, Free Fibonacci Sequences, arXiv preprint arXiv:1403.4614, 2014 and J. Int. Seq. 17 (2014) # 14.8.5
Eric Weisstein's World of Mathematics, Fibonacci nStep


CROSSREFS

Cf. A015134 (orbits of 2step sequences), A106306 (primes that yield a simple orbit structure in 2step recursions).
Sequence in context: A106486 A195743 A106494 * A116619 A091220 A057955
Adjacent sequences: A015132 A015133 A015134 * A015136 A015137 A015138


KEYWORD

nonn


AUTHOR

Phil Carmody


EXTENSIONS

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


STATUS

approved



