Some combinatorial identities via Riordan arrays and k-order Fibonacci matrices

Abstract

In this paper, we investigate some interesting relationships between Riordan arrays and k-order Fibonacci matrices, which provide a unified approach to studying some lower triangular matrices, such as the Fuss-Catalan matrices, harmonic matrices, etc. We give factorizations of the Riordan arrays via the k-order Fibonacci matrices. Moreover, based on matrix representations, various combinatorial identities are derived.