The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A233246 Sum of squares of cycle lengths for different cycles in Fibonacci-like sequences modulo n. 1
 1, 10, 65, 82, 417, 650, 769, 658, 1793, 4170, 1151, 3026, 4705, 7690, 7137, 5266, 10369, 7562, 6319, 19218, 6977, 11510, 25345, 12818, 52417, 47050, 48449, 35410, 11565, 71370, 28351, 42130, 39615, 41482, 81057, 30674, 103969, 25282, 80033 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Here Fibonacci-like means a sequence following the Fibonacci recursion: b(n)=b(n-1)+b(n-2). These sequences modulo n cycle. The number of different cycles is A015134(n). This sequence divided by n^2 is the average cycle length per different starting pairs modulo n, see A233248. If n is in A064414, then a(n)/n^2 is the average distance between two neighboring multiples of n. If n is in A064414, then a(n)/2n^2 is the average distance to the next zero over all starting pairs of remainders. LINKS Table of n, a(n) for n=1..39. 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)=1+9+36+36=82. 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[Total[ Flatten[Table[cl[i, j, n], {i, 0, n - 1}, {j, 0, n - 1}]]], {n, 50}] CROSSREFS Cf. A233248, A064414. Sequence in context: A286070 A033908 A033863 * A229996 A255245 A210369 Adjacent sequences: A233243 A233244 A233245 * A233247 A233248 A233249 KEYWORD nonn AUTHOR Brandon Avila and Tanya Khovanova, Dec 06 2013 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 17 14:56 EDT 2024. Contains 373448 sequences. (Running on oeis4.)