On the properties of iterated binomial transforms for the Padovan and Perrin matrix sequences

TL;DR

This paper explores the properties of iterated binomial transforms applied to Padovan and Perrin matrix sequences, deriving formulas and relationships to deepen understanding of their mathematical structure.

Contribution

It introduces new formulas and relationships for iterated binomial transforms of Padovan and Perrin matrix sequences, expanding theoretical knowledge.

Findings

Derived Binet formulas and generating functions for the transforms

Established relationships between iterated transforms of the sequences

Provided summation formulas using recurrence relations

Abstract

In this study, we apply "r" times the binomial transform to the Padovan and Perrin matrix sequences. Also, the Binet formulas, summations, generating functions of these transforms are found using recurrence relations. Finally, we give the relationships of between iterated binomial transforms for Padovan and Perrin matrix sequences.