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 language | English (US) |
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Pages (from-to) | 29-31 |
Number of pages | 3 |
Journal | Fibonacci Quarterly |
Volume | 57 |
Issue number | 1 |
State | Published - Feb 2019 |
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory