Matrix sequences of special cases of generalized Tribonaccinumbers

The matrix sequences have taken so much interest for different type of numbers. In this thesis, we consider the matrix sequences of special cases of the generalized 3-step Fibonacci (generalized Tribonacci) numbers. We summarize the chapters as follows. In chapter 1, we present some basic important definitions and some results used throughout the thesis. In chapter 2, we define and investigate the Tribonacci and Tribonacci-Lucas matrix sequences. We give Binet's formulas, generating functions, and the summation formulas for these sequences. Moreover, we present some identities and matrices related with these sequences. In chapter 3, we introduce and investigate the adjusted Tribonacci-Lucas matrix sequence. We present Binet's formula, generating function, and the summation formulas for this sequence. Moreover, we give some identities and matrices related with this sequence. In chapter 4, we define and investigate the third-order Pell and third-order Pell-Lucas matrix sequences. We give Binet's formulas, generating functions, and the summation formulas for these sequences. Moreover, we present some identities and matrices related with these sequences. In chapter 5, we define and investigate the Narayana matrix and Narayana-Lucas matrix sequences. We present Binet's formulas, generating functions, and the summation formulas for these sequences. Moreover, we give some identities and matrices related with these sequences.In chapter 6, we introduce and investigate the generalized Narayana matrix sequence and we deal with, in detail, three special cases of this sequence which we call them Narayana, Narayana-Lucas and Narayana-Perrin matrix sequences. We present Binet's formulas, generating functions, and the summation formulas for these sequences.Moreover, we give some identities and matrices related with these sequences. Furthermore, we show that there always exist interrelation between generalized Narayana, Narayana, Narayana-Lucas and Narayana-Perrin matrix sequences. This chapter contains our original work.