Matrix Form of the Iterated Binomial Transforms

Abstract

In a previous paper, we have estudied the Binomial transforms of the k-Fibonacci sequences and later we have studied the iterated Binomial transforms of these sequences. Now we study the matrix form of these four different binomial transforms of integer sequences in such a way that we can find a relation between the terms of the transformed sequence and the terms of the initial sequence. In this form we do not need to find the initial terms of the transformed sequence to find the following term from the application of the corresponding recurrence equation. Later we will apply the obtained results to the particular case of the k-Fibonacci sequence.