Horadam integer and matrix sequences

In this study, after a detailed introduction of the literature concerning the Horadam sequence, information about its most popular ones such as Fibonacci, Lucas, Jacobsthal, Jacobsthal Lucas, Pell and Pell Lucas and their basic features are presented. Besides, polynomial sequence, which is an aggregation of these number sequences, is also introduced. Then, Horadam number and polynomial sequences are analyzed in detail. In the following part, Horadam polynomials and Chebyshev polynomials are associated with each other. Following this, features related with the generalized Horadam sequences are acquired through the use of matrix. Finally, in the last part, after the introduction of Generalized Fibonacci and Generalized Lucas number sequences, and some of their basic features, Generalized Fibonacci, Generalized Lucas and Horadam matrix sequences are examined in detail.