On the Gaussian modified pell numbers

Special number sequences and their generalizations have been studied by many authors. The aim of this thesis is to define Gaussian modified Pell number sequence and to determine some properties of this sequence. Also, by using this definition, it is aimed to define Gaussian modified Pell polynomial sequence and Gaussian (s,t)-modified Pell sequence and to examine some properties of these sequences. This thesis consists of seven chapters. In the first chapter, the history of some special number sequences, especially Fibonacci number sequence, and usage of these number sequences in daily life are mentioned. In the second chapter, some basic concept and definitions needed in the further chapters are given. In the third chapter, the Gaussian modified Pell sequence is defined and some combinatorial properties of this sequence are examined. In the fourth chapter, the Gaussian modified Pell polynomial sequence is defined and some of its properties are discussed. In the fifth chapter, (s,t)-modified Pell sequence which is a generalization of the modified Pell sequence is firstly defined. Then, (s,t)-modified Pell matrix sequence whose components consist of the modified Pell numbers is defined. Some combinatorial properties of these sequences are investigated. In the sixth chapter, Gaussian (s,t)-modified Pell sequence which is a generalization of the Gaussian modified Pell sequence is firstly defined. Then, Gaussian (s,t)-modified Pell matrix sequence whose components consist of the Gaussian modified Pell numbers is defined. Some combinatorial properties of these sequences are discussed. In the last chapter, the main results obtained from the thesis and some proposals are discussed.