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

Year 2025, Volume: 13 Issue: 1, 299 - 316, 30.01.2025

Arzu Özkoç Öztürk , Faruk Kaplan

https://doi.org/10.29130/dubited.1555372

https://izlik.org/JA29US69ZZ

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.

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