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

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.