Sergio Falcon

On the Dual δ − k − Fibonacci Numbers

Sergio Falcon · Asian Research Journal of Mathematics · 2019

We define two integer sequences that depend on a parameter and that are related to each other by two recurrence relations. Then we find the Binet formula for the terms of these sequences and, by developing it, we will get an equivalent combinatorial formula. We show that each seq...

Open access Research Article 10.9734/ARJOM/2019/45436

Iterated Binomial Transforms of the k-Fibonacci Sequence

Sergio Falcon · Journal of Advances in Mathematics and Computer Science · 2014

In this paper, we study the iterated application of the Binomial transform, the k–Binomial transform, the Rising k–Binomial transform, and the Falling k–Binomial transform to the k–Fibonacci sequence. In particular, we obtain the recurrence relation between the terms of the seque...

Open access Research Article 10.9734/BJMCS/2014/11783