Unified tiling proofs of a family of Fibonacci identities

Arthur T. Benjamin, Joshua Crouch, James A. Sellers

Research output: Contribution to journalArticle

Abstract

In a recent work, Baxter and Pudwell mentioned the following identity for the Fibonacci numbers Fn and noted that it can be proven via induction: For all n ≥ 1, F2n = 1 · F2n−2 + 2 · F2n−4 + · · · + (n − 1) · F2 + n. We give a combinatorial proof of this identity and a companion identity. This leads to an infinite family of identities, which are also given combinatorial proofs.

Original languageEnglish (US)
Pages (from-to)29-31
Number of pages3
JournalFibonacci Quarterly
Volume57
Issue number1
StatePublished - Feb 2019
Externally publishedYes

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