Binomial Transforms of the Padovan and Perrin Matrix Sequences

Abstract

We apply the binomial transforms to Padovan and Perrin matrix sequences. Also, the Binet formulas, summations, and generating functions of these transforms are found by recurrence relations. Finally, we illustrate the relations between these transforms by deriving new formulas.

Binomial Transform of the Generalized Fourth Order Pell Sequence

“…For recent works on binomial transform of well-known sequences, see for example, [21,22,23,24,25,26,27,28,29,30,31,32,33].…”

On Binomial Transform of the Generalized Fifth Order Pell Sequence

“…For recent works on binomial transform of well-known sequences, see for example, [13,14,15,16,17,18,19,20,21,22,23,24,25].…”

De Moivre-Type Identities for the Padovan Numbers

“…The characteristic equation of the Padovan Sequence is 𝑥𝑥 3 − 𝑥𝑥 − 1 = 0. The real root of this characteristic equation is known as plastic ratio which was defined in 1924 by G´erard Cordonnier, [5].…”