Type: Article
Publication Date: 2009-02-02
Citations: 3
DOI: https://doi.org/10.1088/1751-8113/42/8/085005
We study the behaviour of generalized random Fibonacci sequences defined by the relation gn = |λgn−1 ± gn−2|, where the ± sign is given by tossing an unbalanced coin, giving probability p to the + sign. We prove that the expected value of gn grows exponentially fast for any 0 < p ⩽ 1 when λ ⩾ 2, and for any p > (2 − λ)/4 when λ is of the form 2cos(π/k) for some fixed integer k ⩾ 3. In both cases, we give an algebraic expression for the growth rate.