k Sequences of Generalized Van der Laan and Generalized Perrin Polynomials

TL;DR

This paper introduces generalized k sequences of Van der Laan and Perrin polynomials derived from Fibonacci and Lucas polynomials, exploring their properties and interrelationships.

Contribution

It presents new generalized polynomial sequences and numbers, extending classical Van der Laan and Perrin sequences, with detailed properties and relationships.

Findings

Defined k sequences of generalized Van der Laan and Perrin polynomials

Derived generalized order-k Van der Laan and Perrin numbers

Explored relationships between these sequences and polynomials

Abstract

In this paper, we present k sequences of Generalized Van der Laan Polynomials and Generalized Perrin Polynomials using Genaralized Fibonacci and Lucas Polynomials. We give some properties of these polynomials. We also obtain generalized order-k Van der Laan Numbers, k sequences of generalized order-k Van der Laan Numbers, generalized order-k Perrin Numbers and k sequences of generalized order-k Perrin Numbers. In addition, we examine the relationship between them.