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
M13 9PL
United Kingdom


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.

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(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.

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