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A233248 The average cycle length of cycles in Fibonacci-like 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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 1 10:03 EDT 2020. Contains 333159 sequences. (Running on oeis4.)