2008/03/19 by Eduardo H. M. Brietzke, Brietzke, Eduardo H. M.
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #math.CO #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.0803.2803
Accepted for publication in Discrete Mathematics
arxiv created 2008/03/19 · openalex publication_date 2008/03/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider an identity relating Fibonacci numbers to Pascal's triangle discovered by G. E. Andrews. Several authors provided proofs of this identity, most of them rather involved or else relying on sophisticated number theoretical arguments. We present a new proof, quite simple and based on a Riordan array argument. The main point of the proof is the construction of a new Riordan array from a given Riordan array, by the elimination of elements. We extend the method and as an application we obtain other identities, some of which are new. An important feature of our construction is that it establishes a nice connection between the generating function of the A-sequence of a certain class of Riordan arrays and hypergeometric functions.