#### Publication Date

5-1-2001

#### Degree Program

Department of Mathematics and Computer Science

#### Degree Type

Master of Science

#### Abstract

The familiar Fibonacci sequence 1,1,2,3,5,8,13,... can be described by the recurrence relation x(0) = 1, x(1) = 1, x(n) = x(n-1) + x(n-2). For this relation, as n → oo, x(n+1) → 1 +√5 x(n) 2 ' which is the familiar golden ratio. This value is also the dominant eigenvalue of the above recurrence relation. In this series, we consider the dominant eigenvalue of some Fibonacci-like sequence of the form x(n) = ∑n-1/k+1 ak Zk (n-k) where the Zk's are independent random variables with Zk = {+1 with probability p - 1 with probability q, with p + q = 1, and for each k, the ak's are either 0 or 1.

#### Disciplines

Mathematics

#### Recommended Citation

Hurst, Elyssa, "Elgenvalues of Fibonacci-like Sequences" (2001). *Masters Theses & Specialist Projects.* Paper 668.

https://digitalcommons.wku.edu/theses/668