A new generalization of Fibonacci and Lucas sedenions

The main purpose of this thesis is to investigate the basic properties of these sequences by defining sedenions whose components are integers, that is, defining a generalization of Fibonacci and Lucas sedenions. In the first part, the purpose of the thesis and the references we used in the thesis were mentioned. In the second chapter, the definitions and basic concepts required for the thesis are mentioned. In the third chapter, the definitions of Fibonacci and Lucas sedenions, Binet formulas, exponential generating functions, Catalan, Cassini, d'Ocagne identities and some binomial sum formulas including these sedenions are given. In the fourth chapter, some special cases for the Fibonacci and Lucas sedenions are mentioned. And it has been shown that the results obtained from these special cases are transformed into Fibonacci sedenion, Lucas sedenion, Fibonacci sedenion, Lucas sedenion, Pell sedenion, Pell Lucas sedenion, Pell sedenion, Pell Lucas sedenion, Jacobsthal sedenion and Jacobsthal Lucas sedenion. Then, Binet formulas, exponential generating functions, Catalan, Cassini, d'Ocagne idenities and some binomial sum formulas including these sedenions are given respectively.