The generating functions of number and matrix sequences

In this study, we define special integer sequences such as Fibonacci, Lucas, Pell, Pell Lucas, Jacobsthal, Jacobsthal Lucas sequences briefly and give some their basic properties. And then different generalizations of these sequences are obtained and the generating functions of the sespecial integer sequences and their generalized sequences are given. By using the above integer sequences polynomial and matrix sequences and also their generalized polynomialand matrix sequences are obtained and then their generating functions are found. After that exponential generating functionsare defined. And by using exponential generating functions Some properties of Fibonacci, Lucas, Jacobsthal, Jacobsthal Lucas sequences are found. Moreever, some properties of these sequences are obtained by using different type of generating functions. Keywords: Special integer sequences, Generalized Integer and Matrix sequences, Generating Functions, Binet Formula.