A Note Concerning Generalized Complex k-Horadam and Generalized Gaussian k-Horadam Squences

Abstract

In this paper, we have studied the generalized Complex k-Horadam and generalized Gaussian k-Horadam sequences. We have given the generating functions and Binet formulas of generalized Complex k-Horadam and generalized Gaussian k-Horadam sequences. Moreover, we have obtained some important identities involving the generalized Complex k-Horadam and generalized Gaussian k-Horadam numbers.

On Gaussian Jacobsthal-Padovan Numbers

“…Gaussian forms of these sequences are also available in the literature. Gaussian forms of these sequences as well as their properties have been inquired into by many authors, see [6][7][8][9][10] for details. In [9], Jacobsthal and Jacobsthal-Lucas sequences' Gaussian forms are defined by the recursion formulas…”