On generating matrices of the k-Pell, k-Pell-Lucas and modified k-Pell sequences

Abstract

In this paper we define some tridiagonal matrices depending of a parameter from which we will find the k-Pell, k-Pell-Lucas and Modified k-Pell numbers.Mathematics Subject Classification: 11B37, 11B83.

On Hybrid Hyper k-Pell, k-Pell–Lucas, and Modified k-Pell Numbers

“…The proof of the identity ( 16) can be performed in a similar way to what we have just shown, taking into account the respective initial conditions. As for the last generating function, all we have to do is look at Item 1 of Proposition 3 in [14], and the result follows immediately.…”

“…Motivated by the hyper Fibonacci numbers, in [14] was introduced the "hyper" approach for the k-Pell, k-Pell-Lucas, and Modified k-Pell sequences. The authors established some properties and discussed the concavity, convexity, log-concavity, and log-convexity properties for these sequences.…”

“…Consider the hyper k-Pell, the hyper k-Pell-Lucas, and the hyper Modified k-Pell numbers that were introduced by Catarino, Alves, and Campos in [14]. Some properties and identities satisfied by these sequences are present in [14]. In this paper, it is our intention to introduce new sequences that are the "hybrid version" of them.…”

“…As we have mentioned before, in this section, we recall the hyper k-Pell, k-Pell-Lucas, and Modified k-Pell sequences introduced in [14] and present some properties that will be necessary for the study of the new sequences introduced in the next section of this paper.…”

On Generating Tridiagonal Matrices of Generalized (s,t)-Pell, (s,t)-Pell Lucas and (s,t)-Modified Pell Sequences

“…Falcon displayed some equalities of k-Fibonacci numbers with the determinant of some special matrices in [12]. Catarino obtained the n-th elements of k-Pell, k-Pell-Lucas, and modified k-Pell sequences by the determinants of some tridiagonal matrices in [13]. In [14], properties of hyperbolic generalized Pell numbers are studied.…”