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k-Grahaml Sequences and Special Relations

  • Hakan Akkuş 1,   
  • Engin Özkan 2,*

Received: 14 Mar 2026 | Revised: 05 Apr 2026 | Accepted: 18 Apr 2026 | Published: 22 Apr 2026

Abstract

In this study, we define the k-Grahaml, k-Grahaml-Lucas, and Modified k-Grahaml sequences and certain terms from these sequences are given. We then determine the generating functions, evaluate the summations, and derive the related expressions. We also relate the terms of these sequences to matrices and carry out various matrix-related computations. We express the Binet formulas of these sequences in different ways. In addition, we further study the interrelations between various forms of Grahaml-type sequences, including k-Grahaml, k-Grahaml-Lucas, and their modified versions. Finally, we discover an intriguing relationship between the k-Grahaml sequence and the Grahaml-Lucas sequence.

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Akkuş, H.; Özkan, E. k-Grahaml Sequences and Special Relations. Journal of Applied Mathematics, Mechanics and Engineering 2026, 1 (1), 3.
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