Curtis Heberle
Thesis
A Combinatorial Approach to $r$-Fibonacci Numbers
- Advisor
- Arthur T. Benjamin
- Second Reader(s)
- Kimberly Kindred
Abstract
In this paper we explore generalized “$r$-Fibonacci Numbers” using a combinatorial “tiling” interpretation. This approach allows us to provide simple, intuitive proofs to several identities involving $r$-Fibonacci Numbers presented by F.T. Howard and Curtis Cooper in the August, 2011, issue of the Fibonacci Quarterly. We also explore a connection between the generalized Fibonacci numbers and a generalized form of binomial coefficients.
