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
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.
Recommended Citation
Heberle, Curtis, "A Combinatorial Approach to $r$-Fibonacci Numbers" (2012). HMC Senior Theses. 34.
https://scholarship.claremont.edu/hmc_theses/34
