Binomial Transforms Of The K-lucas Sequences And Its Properties

Abstract

In this paper, we employ several class of transforms like binomial, k-binomial and rising transforms to the k-Lucas sequence. Moreover, we investigate some interesting properties between the so-obtained new sequences and the k-Lucas sequence.

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].…”

On the Properties of Iterated Binomial Transforms for the Padovan and Perrin Matrix Sequences

“…In [13,15], authors gave the application of the several class of transforms to the k-Fibonacci and k-Lucas sequence. In [14], the authors applied the binomial transforms to the Padovan (P n ) and Perrin matrix sequences (R n ).…”