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1. Generalized Fibonacci Numbers Through Tilings and Markov Chains
Arthur Benjamin, Christopher Hanusa, and Francis Su.
Published in Utilitas Mathematica, Volume 64, pp 3-17. (2003)
Available for download in pdf.

Abstract: We present a tiling interpretation for kth order linear recurrences, which yields new combinatorial proofs for recurrence identities. Moreover, viewing the tiling process as a Markov chain also yields closed form Binet-like expressions for these recurrences.

No supplementary materials.

 

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