Geodesic
A restricted random walk defined via a Fibonacci process
Journal of integer sequences, Tome 14 (2011) no. 5
In this article we study a random walk on a particularly simple graph. This walk is determined by a probabilistic process associated with the Fibonacci sequence. Exact formulas are derived for the expected proportions of time spent on each arc of the graph for a walk of length $n$, giving rise to sequences that do not appear in Sloane's On-Line Encyclopedia of Integer Sequences. We also obtain asymptotic relations for these expected proportions.
Classification : 05A15, 05A16, 05C81, 11B39
Keywords: random walks, Fibonacci numbers, generating functions, probabilities 
@article{JIS_2011__14_5_a5,
     author = {Griffiths,  Martin},
     title = {A restricted random walk defined via a {Fibonacci} process},
     journal = {Journal of integer sequences},
     year = {2011},
     volume = {14},
     number = {5},
     zbl = {1217.05024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2011__14_5_a5/}
}
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Griffiths,  Martin. A restricted random walk defined via a Fibonacci process. Journal of integer sequences, Tome 14 (2011) no. 5. http://geodesic.mathdoc.fr/item/JIS_2011__14_5_a5/