Tetranacci and Tetranacci-Lucas Quaternions
Yüksel Soykan *
Department of Mathematics, Art and Science Faculty, Zonguldak Bulent Ecevit University, 67100, Zonguldak, Turkey.
*Author to whom correspondence should be addressed.
Abstract
The quaternions form a 4-dimensional Cayley-Dickson algebra. In this paper, we introduce the Tetranacci and Tetranacci-Lucas quaternions. Furthermore, we present some properties of these quaternions and derive relationships between them. We present the generating functions, Binet's formulas and sums formulas of these quaternions. Moreover, we give matrix formulation of Tetranacci and Tetranacci-Lucas quaternions.
Keywords: Tetranacci numbers, quaternions, Tetranacci quaternions, Tetranacci-Lucas quaternions.