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)|
|Number of pages||3|
|State||Published - Feb 2019|