Nazmiye Yilmaz

Matrix Sequences in terms of Padovan and Perrin Numbers

The first main idea of this paper is to develop the matrix sequences that represent Padovan and Perrin numbers. Then, by taking into account matrix properties of these new matrix sequences, some behaviours of Padovan and Perrin numbers will be investigated. Moreover, some important relationships between Padovan and Perrin matrix sequences will be presented.

The Generalized (s,t)‐Sequence and its Matrix Sequence

In this study, we first define a new sequence in which it generalizes (s,t)‐Fibonacci and (s,t)‐Lucas sequences at the same time. After that, by using it, we establish generalized (s,t)‐matrix sequences. Finally we present some important relationships among this new generalization, (s,t)‐Fibonacci and (s,t)‐Lucas sequences and their matrix sequences.

Incomplete Tribonacci–Lucas Numbers and Polynomials

In this paper, we define Tribonacci–Lucas polynomials and present Tribonacci–Lucas numbers and polynomials as a binomial sum. Then, we introduce incomplete Tribonacci–Lucas numbers and polynomials. In addition we derive recurrence relations, some properties and generating functions of these numbers and polynomials. Also, we find the generating function of incomplete Tribonacci polynomials which is given as the open problem in [12].

On the Binomial Sums of k‐Fibonacci and k ‐Lucas sequences

The main purpose of this paper is to establish some new properties of k‐Fibonacci and k‐Lucas numbers in terms of binomial sums. By that, we can obtain these special numbers in a new and direct way. Moreover, some connections between k‐Fibonacci and k‐Lucas numbers are revealed to get a more strong result.

On properties of bi-periodic Fibonacci and Lucas polynomials

In this paper, we define bi-periodic Fibonacci and Lucas polynomials and investigate properties of these polynomials which generalized of bi-periodic Fibonacci and Lucas numbers. We also obtain some new algebraic properties on these numbers and polynomials.

The Construction of Horadam Numbers in Terms of the Determinant of Tridiagonal Matrices

In this study, by using determinants of tridiagonal matrices, we mainly obtain Horadam numbers with positive and negative indices. Therefore we establish a new generalization for the tridiagonal matrices that represent well known numbers such as Fibonacci, Lucas, Jacobsthal, Jacobsthal‐Lucas, Pell and Pell‐Lucas numbers.