Geodesic
On the average growth of random Fibonacci sequences
Journal of integer sequences, Tome 10 (2007) no. 2
Zbl   EuDML
We prove that the average value of the $n$-th term of a sequence defined by the recurrence relation $g_{n} = |g_{n-1} \pm g_{n-2}$|, where the $\pm $ sign is randomly chosen, increases exponentially, with a growth rate given by an explicit algebraic number of degree 3. The proof involves a binary tree such that the number of nodes in each row is a Fibonacci number.
Classification : 11A55, 15A52, 05C05, 15A35
Keywords: binary tree, random Fibonacci tree, linear recurring sequence, random Fibonacci sequence, continued fraction 
Rittaud,  Benoît. On the average growth of random Fibonacci sequences. Journal of integer sequences, Tome 10 (2007) no. 2. http://geodesic.mathdoc.fr/item/JIS_2007__10_2_a0/
@article{JIS_2007__10_2_a0,
     author = {Rittaud,  Beno{\^\i}t},
     title = {On the average growth of random {Fibonacci} sequences},
     journal = {Journal of integer sequences},
     year = {2007},
     volume = {10},
     number = {2},
     zbl = {1127.11013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2007__10_2_a0/}
}
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