k-Jacobsthal and k-Jacobsthal Lucas generalized octonions

In this thesis, Jacobsthal and Jacobsthal lucas sequence and their forms containing specific cases of definition, some identities,dicussed and some new results are obtained for these sequence. The thesis consists of five chapters. In the first chapter, information about the famous integer numbers of the second order linear recurrence,the Fibonacci, Fibonacci lucas, Pell and Pell lucas numbers. This sequences have many identites,properties and aplications with related to this sequences. In the second chapter, we remind the basic definitions and theorms related to Jacobsthal and Jacobsthal lucas sequence. The third chapter we remind the Generalized Jacobsthal sequence. The fourth chapter we investigate Horadam octonions with coefficients from Horadam sequence. In the fifth chapter the original chapter of thesis,in the first section, the h(x)-Jacobsthal octonion polynomials with some identities are given. In the second sectio, we investigate k-Jacobsthal and k-Jacobsthal lucas generalized octonions and give some properties of them.