A New Approach to k-Oresme and k-Oresme-Lucas Sequences

In this study, the k-Oresme and k-Oresme-Lucas sequences are defined, and some terms of these sequence are given. Then, the relations between the terms of the k-Oresme and k-Oresme-Lucas sequences are presented. In addition, we give these sequences the Binet formulas, generating functions, Cassini identity, Catalan identity etc. Moreover, the k-Oresme and k-Oresme-Lucas sequences are associated with Fibonacci, Pell numbers and Lucas, and Pell- Lucas numbers, respectively. Finally, the Catalan transforms of these sequences are given and Hankel transforms are applied to these Catalan sequences and associated with the terms of the sequence.