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Curtis Heberle

Picture of 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.

Additional Materials

Poster