Identities for generalized Fibonacci numbers: a combinatorial approach

Abstract

This note shows a combinatorial approach to some identities for generalized Fibonacci numbers. While it is a straightforward task to prove these identities with induction, and also by arithmetical manipulations such as rearrangements, the approach used here is quite simple to follow and eventually reduces the proof to a counting problem.

Keywords:

• generalized Fibonacci numbers
• combinatorial proof
• non-inductive methods