Mathematics – Combinatorics
Scientific paper
2008-03-19
Mathematics
Combinatorics
Accepted for publication in Discrete Mathematics
Scientific paper
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.
No associations
LandOfFree
An Identity of Andrews and a New Method for the Riordan Array Proof of Combinatorial Identities does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with An Identity of Andrews and a New Method for the Riordan Array Proof of Combinatorial Identities, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and An Identity of Andrews and a New Method for the Riordan Array Proof of Combinatorial Identities will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-323157