Open Access Senior Thesis
Bachelor of Science
The Fibonacci Numbers are one of the most intriguing sequences in mathematics. I present generalizations of this well known sequence. Using combinatorial proofs, I derive closed form expressions for these generalizations. Then using Markov Chains, I derive a second closed form expression for these numbers which is a generalization of Binet’s formula for Fibonacci Numbers. I expand further and determine the generalization of Binet’s formula for any kth order linear recurrence.
Hanusa, Christopher, "Continued Fractions and their Interpretations" (2001). HMC Senior Theses. 127.