Open Access Senior Thesis
Bachelor of Science
Arthur T. Benjamin
This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.
© Curtis Heberle
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.
Heberle, Curtis, "A Combinatorial Approach to $r$-Fibonacci Numbers" (2012). HMC Senior Theses. 34.