STRUCTURAL PROPERTIES AND SPECIAL TRANSFORMATIONS k- COPPER FIBONACCI AND k-COPPER LUCAS SEQUENCES

In this study, we define the k-Copper Fibonacci and k-Copper Lucas sequences, and the first few terms of these sequences are given. Then we obtain properties such as special generating functions, Binet formulas, etc. Also, we present special relations between these sequences and the roots of their characteristic equations. We obtain the relationship between the ratio of the biggest to the smallest of two consecutive terms of these sequences. In addition, we give important relations among the positive and negative index terms of these sequences, and the sum of the squares of two consecutive terms is related to these sequences. We calculate the significant identities of these sequences. Besides, we apply Catalan transformations of these sequences and obtain the first few terms. We present some features of these Catalan transformations, such as generating functions. Furthermore, we apply the Hankel transform to the Catalan transform of these sequences.