In this study, two sequences called (s, t)-Jacobsthal, (s, t)-Jacobsthal Lucas are defined by considering the usual Jacobsthal and Jacobsthal Lucas numbers. After that, we establish some properties of these sequences and some important relationships between (s, t)-Jacobsthal sequence and (s, t)-Jacobsthal Lucas sequence.

In this study, we bring into light a new generalization of the Jacobsthal Lucas numbers, which shall also be called the bi-periodic Jacobsthal Lucas sequence as   with initial conditions $$\ \hat{c}_{0}=2,\ \hat{c}_{1}=a.$$ The Binet formula as well as the generating function for this sequence are given. The convergence property of the consecutive terms of this sequence is examined after which the well known Cassini, Catalan and the D'ocagne identities as well as some related summation formulas are also given.

In this study, we consider sequences named k-Jacobsthal, k-Jacobsthal Lucas sequences. After that, by using these sequences, we define k-Jacobsthal and k-Jacobsthal-Lucas matrix sequence at the same time. Finally we investigate some properties of these sequences, present some important relationship between k-Jacobsthal matrix sequence and k-Jacobsthal Lucas matrix sequence.

In this study, we consider sequences named .s; t/-Jacobsthal, .s; t/-Jacobsthal-Lucas and defined generalized .s; t/-Jacobsthal integer sequences. After that, by using these sequences, we define generalized .s; t/-Jacobsthal matrix sequence in which it generalizes .s; t/-Jacobsthal matrix sequence; .s; t/-JacobsthalLucas matrix sequence at the same time. Finally we investigate some properties of the sequence and present some important relationship among .s; t/-Jacobsthal matrix sequence, .s; t/-Jacobsthal-Lucas matrix sequence and generalized .s; t/-Jacobsthal matrix sequence. IntroductionWe can find a great deal of study on the different integer sequences in [1,2,8,9,11]. Many properties of these sequences were deduced directly from elementary matrix algebra. For example, Köken and Bozkurt [7] defined a Jacobsthal matrix of the type nxn and using this matrix derived a lot of properties on Jacobsthal numbers. Of course the most known integer sequence is made of Fibonacci numbers which are very important because of golden section. So the authors are interested in Fibonacci matrix sequences. Civciv and Turkmen,in [3,4], defined .s; t/-Fibonacci and .s; t/-Lucas matrix sequences by using .s; t/-Fibonacci and .s; t/-Lucas sequences.Jacobsthal and Jacobsthal-Lucas numbers are defined for n 1 by recurrence relations j nC1 D j n C 2j n 1 ; j 0 D 0; j

In this paper, we define a new generalization for Pell and Pell Lucas, and modified Pell sequences called generalized Vieta-Pell and Vieta-Pell-Lucas polynomial sequences. The Binet formulae, generating functions, sum formulas, differatation rules and some important properties for these sequences are given. And then we generate a matrix whose elements are of generalized Vieta-Pell terms. By using this matrix we derive some properties for generalized Vieta-Pell and generalized Vieta-Pell-Lucas polynomial sequences