

A233248


The average cycle length of cycles in Fibonaccilike sequences modulo n over all starting pairs of remainders.


2



1, 2, 7, 5, 17, 18, 16, 10, 22, 42, 10, 21, 28, 39, 32, 21, 36, 23, 18, 48, 16, 24, 48, 22, 84, 70, 66, 45, 14, 79, 30, 41, 36, 36, 66, 24, 76, 18, 53, 50, 40, 40, 88, 28, 93, 48, 32, 24, 110, 210, 68, 80, 108, 67, 20, 47, 66, 34, 58, 91, 60, 30
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OFFSET

1,2


COMMENTS

a(n) = Round(A233246(n)/n^2.
If n is in A064414, then a(n) is the average distance between two neighboring multiples of n.
If n is in A064414, then a(n)/2 is the average distance to the next zero over all starting pairs of remainders.


LINKS

Table of n, a(n) for n=1..62.
B. Avila and T. Khovanova, Free Fibonacci Sequences, arXiv preprint arXiv:1403.4614, 2014 and J. Int. Seq. 17 (2014) # 14.8.5


EXAMPLE

For n=4 there are four possible cycles: A trivial cycle of length 1: 0; two cycles of length 6: 0,1,1,2,3,1; and a cycle of length 3: 0,2,2. Hence, a(4)=Round((1+9+36+36)/16)=5.


MATHEMATICA

cl[i_, j_, n_] := (step = 1; first = i; second = j;
next = Mod[first + second, n];
While[second != i  next != j, step++; first = second;
second = next; next = Mod[first + second, n]]; step)
Table[Round[
Total[Flatten[Table[cl[i, j, n], {i, 0, n  1}, {j, 0, n  1}]]]/
n^2], {n, 70}]


CROSSREFS

Cf. A233246, A064414
Sequence in context: A100792 A096037 A286379 * A114025 A135566 A100759
Adjacent sequences: A233245 A233246 A233247 * A233249 A233250 A233251


KEYWORD

nonn


AUTHOR

Brandon Avila and Tanya Khovanova, Dec 06 2013


STATUS

approved



