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.
| Identifer | oai:union.ndltd.org:CLAREMONT/oai:scholarship.claremont.edu:hmc_theses-1033 |
| Date | 31 May 2012 |
| Creators | Heberle, Curtis |
| Publisher | Scholarship @ Claremont |
| Source Sets | Claremont Colleges |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | HMC Senior Theses |
| Rights | © Curtis Heberle, http://creativecommons.org/licenses/by-nc-sa/3.0/ |
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