TOPICS
Rittaud Constant
For any fixed 
and 
(not both equal to zero), define 
as the mean value of the 
th term of a random
Fibonacci sequence starting from 
and 
. Then the ratio 
tends to a constant 
, where 
has the value
 |  |  |
(1)
|
 |  |  |
(2)
|
(OEIS A137421; Rittaud 2007, Janvresse et al. 2008, Finch 2024), where 
denotes the first (and in this case only real) root
of the polynomial 
.
This number may be termed the Rittaud constant.
See also
Random Fibonacci SequenceExplore with Wolfram|Alpha
References
Finch, S. R. "Errata and Addenda to Mathematical Constants." 27 May 2024. https://arxiv.org/abs/2001.00578.Janvresse, E.; Rittaud, B.; and de la Rue, T. "Growth Rate for the Expected Value of a Generalized Random Fibonacci Sequence." 15 Apr 2008. https://arxiv.org/abs/0804.2400.Rittaud, B. "On the Average Growth of Random Fibonacci Sequences." J. Integer Seq. 10, Article 07.2.4, 2007. https://cs.uwaterloo.ca/journals/JIS/VOL10/Rittaud2/rittaud11.html.Rittaud, B.; Janvresse, E.; Lesigne, E. and Novelli, J.-C. Quand les maths se font discrètes. Le Pommier, p. 119, 2008.Sloane, N. J. A. Sequence 137421 A in "The On-Line Encyclopedia of Integer Sequences."Cite this as:
Weisstein, Eric W. "Rittaud Constant." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/RittaudConstant.html