Date of Award
5-31-2012
Document Type
Open Access Senior Thesis
Degree Name
Bachelor of Science
Department
Mathematics
First Thesis Advisor
Arthur T. Benjamin
Second Thesis Advisor
Kimberly Kindred
Rights Information
© Curtis Heberle
Terms of Use & License Information
This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.
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.
Recommended Citation
Heberle, Curtis, "A Combinatorial Approach to $r$-Fibonacci Numbers" (2012). HMC Senior Theses. Paper 34.
http://scholarship.claremont.edu/hmc_theses/34