Graduation Year

2012

Document Type

Open Access Senior Thesis

Degree Name

Bachelor of Science

Department

Mathematics

Reader 1

Arthur T. Benjamin

Reader 2

Kimberly Kindred

Terms of Use & License Information

Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Rights Information

© Curtis Heberle

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.

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