login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A106289 Number of different orbit lengths of the 4-step recursion mod n. 1

%I #11 Mar 24 2024 07:57:18

%S 1,2,2,3,2,4,4,4,4,4,3,5,3,8,3,5,3,8,3,5,7,4,4,7,3,6,6,9,4,6,2,6,6,6,

%T 6,10,5,6,6,6,5,14,2,6,5,8,3,9,7,4,6,7,2,12,5,12,6,7,4,7,3,4,8,7,5,8,

%U 4,7,7,12,3,14,4,10,4,8,10,12,2,7,8,6,2,15,6,3,8,8,2,10,8,9,3,6,6,11,2,14,8

%N Number of different orbit lengths of the 4-step recursion mod n.

%C Consider the 4-step recursion x(k)=x(k-1)+x(k-2)+x(k-3)+x(k-4) mod n. For any of the n^4 initial conditions x(1), x(2), x(3) and x(4) in Zn, the recursion has a finite period. Each of these n^4 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, 5, 10 and 20. The maximum possible length of an orbit is the period of the Fibonacci 4-step sequence mod n, which is essentially A106295(n).

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Fibonaccin-StepNumber.html">Fibonacci n-Step Number</a>.

%Y Cf. A106286 (orbits of 4-step sequences).

%K nonn,changed

%O 1,2

%A _T. D. Noe_, May 02 2005

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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)