In this study, Catalan transformation 𝐶𝑆 𝑘,𝑛 of 𝑘−Jacobsthal-Lucas sequences 𝑆 𝑘,𝑛 is defined. In addition, the transformation of C𝑆 𝑘,𝑛 is written as the product of the Catalan matrix C which is the lower triangular matrix and the 𝑆 𝑘 matrix of type 𝑛 𝑥 1, and the Hankel transformations of some 𝑘−Jacobsthal-Lucas numbers is found.
In this study, firstly the k-Chebsyhev sequence is defined, and some terms of this sequence are given. Then, the relations between the terms of the k-Chebsyhev sequence are presented and the generating function of this sequence is obtained. In addition, the Catalan transformation of the sequence is given and the generating function of the Catalan k-Chebsyhev sequence is obtained. Finally, the Hankel transform is applied to the Catalan k-Chebsyhev transform.
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