On Gaussian Quadra Fibona-Pell Sequence and A Quaternion Sequence Formed by the Terms of This Sequence

Authors : Arzu Özkoç Öztürk, Faruk Kaplan

Pages : 299-316

Doi:10.29130/dubited.1555372

View : 45 | Download : 36

Publication Date : 2025-01-30

Article Type : Research Paper

Abstract :In this study, the Gaussian quadra Fibona-Pell sequence is proposed and examined. The quadra Fibona-Pell sequence is first extended to define the Gaussian quadra Fibona-Pell sequence. Then the generating function, Binet-like formula, and some identities are represented. In addition, some formulas related to the Gaussian quadra Fibona-Pell sequence and some matrices containing terms of the sequence are studied. Finally we define a quaternion sequence formed by the terms of Gaussian quadra Fibona-Pell sequence.
Keywords : Fourth-order recurrence relation, Gaussian numbers, Quaternion.