Journal of Integer Sequences, Vol. 14 (2011), Article 11.5.4

A Restricted Random Walk defined via a Fibonacci Process


Martin Griffiths
School of Education
University of Manchester
Manchester
M13 9PL
United Kingdom

Abstract:

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.


Full version:  pdf,    dvi,    ps,    latex    


(Concerned with sequences A000045 A023607 A023610.)


Received October 10 2010; revised version received April 24 2011. Published in Journal of Integer Sequences, May 2 2011.


Return to Journal of Integer Sequences home page