Webb & Parberry proved in 1969 a startling trigonometric identity involving Fibonacci numbers. This identity has remained isolated up to now, despite the amount of work on related polynomials. We provide a wide generalization of this identity together with what we believe (and hope!) to be its proper understanding.

As in [2], our goal in this article is to write some more prominent and fundamental identities regarding Fibonacci numbers as binomial sums.

We present some binomial identities for sums of the bivariate Fi-bonacci polynomials and for weighted sums of the usual Fibonacci polynomials with indices in arithmetic progression.

In a recent paper, Goyt and Sagan studied distributions of certain set partition statistics over pattern restricted sets of set partitions that were counted by the Fibonacci numbers. Their study produced a class of q-Fibonacci numbers, which they related to q-Fibonacci numbers studied by Carlitz and Cigler. In this paper we will study the distributions of some Mahonian statistics over pattern r...

We study two remarkable identities of Andrews relating Fibonacci numbers and binomial coefficients in terms of generating functions and Riordan arrays. We thus give a deeper insight to the problem and find several new identities involving many other well-known sequences.

We derive a collection of identities for bivariate Fibonacci and Lu-cas polynomials using essentially a matrix approach as well as properties of such polynomials when the variables x and y are replaced by polynomials. A wealth of combinatorial identities can be obtained for selected values of the variables.

We investigate general properties of number sequences which allow explicit representation in terms of products. We find that such sequences form whole families of number sequences sharing similar recursive identities. Applying the proposed identities to power sequences and the sequence of Pochhammer numbers, we recover and generalize known recursive relations. Restricting to the cosine of fract...