Generalized r-Pell and r-Pell-lucas sequences

Pell and Pell-Lucas sequences are two well-known sequences among integer sequences. There are many studies in the literature on the generalizations of these two sequences. One of them is the r–Pell numbers defined by Brod (2019). In this thesis, first of all, r–Pell–Lucas numbers suitable for r–Pell numbers are defined, their generating functions and Binet formulas for these two integer sequences are obtained. A new generalization of the Pell and Pell–Lucas number sequences is needed to obtain simpler results. After this second generalization is named as the 2nd type, many identities are obtained, such as Vajda's, Catalan's, Cassini's and d'Ocagne's identities, for these four number sequences.