The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A106288 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A106288

Number of different orbit lengths of the 3-step recursion mod n.
(history; published version)

#11 by Amiram Eldar at Sun Mar 24 07:57:01 EDT 2024

STATUS

editing

approved

#10 by Amiram Eldar at Sun Mar 24 07:56:59 EDT 2024

LINKS

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

STATUS

reviewed

editing

#9 by Joerg Arndt at Sun Mar 24 05:50:42 EDT 2024

STATUS

proposed

reviewed

#8 by Michel Marcus at Sun Mar 24 04:02:12 EDT 2024

STATUS

editing

proposed

#7 by Michel Marcus at Sun Mar 24 04:02:09 EDT 2024

LINKS

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

STATUS

approved

editing

#6 by Russ Cox at Fri Mar 30 17:22:35 EDT 2012

AUTHOR

_T. D. Noe (noe(AT)sspectra.com), _, May 02 2005

Discussion

Fri Mar 30

17:22

OEIS Server: https://oeis.org/edit/global/120

#5 by N. J. A. Sloane at Sun Jul 11 03:00:00 EDT 2010

LINKS

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

KEYWORD

nonn,new

nonn

#4 by N. J. A. Sloane at Fri Feb 27 03:00:00 EST 2009

COMMENTS

Consider the 3-step recursion x(k)=x(k-1)+x(k-2)+x(k-3) mod n. For any of the n^3 initial conditions x(1), x(2) and x(3) in Zn, the recursion has a finite period. Each of these n^3 vectors belongs to exactly one orbit. In general, there are only a few different orbit lengths for each n. For n=8, there are 5 different lengths: 1, 2, 4, 8, and 16. The maximum possible length of an orbit is A046738(n), the period of the Fibonacci 3-step sequence mod n.

KEYWORD

nonn,new

nonn

#3 by N. J. A. Sloane at Sun Jun 29 03:00:00 EDT 2008

LINKS

E. W. Eric Weisstein, 's World of Mathematics, <a href="http://mathworld.wolfram.com/Fibonaccin-Step.html">The World of Mathematics: Fibonacci n-Step</a>

KEYWORD

nonn,new

nonn

#2 by N. J. A. Sloane at Fri Feb 24 03:00:00 EST 2006

COMMENTS

Consider the 3-step recursion x(k)=x(k-1)+x(k-2)+x(k-3) mod n. For any of the n^3 initial conditions x(1), x(2), and x(3) in Zn, the recursion has a finite period. Each of these n^3 vectors belongs to exactly one orbit. In general, there are only a few different orbit lengths for each n. For n=8, there are 5 different lengths: 1, 2, 4, 8, and 16. The maximum possible length of an orbit is A046738(n), the period of the Fibonacci 3-step sequence mod n.

KEYWORD

nonn,new

nonn