On complex Leonardo numbers

Adnan Karataş
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 28, 2022, Number 3, Pages 458–465
DOI: 10.7546/nntdm.2022.28.3.458-465
Full paper (PDF, 149 Kb)

Details

Authors and affiliations

Adnan Karataş
Department of Mathematics, Faculty of Arts and Sciences, Pamukkale University
Denizli, Turkey

Abstract

In this study, we introduce the complex Leonardo numbers and give some of their properties including Binet formula, generating function, Cassini and d’Ocagne’s identities. Also, we calculate summation formulas for complex Leonardo numbers involving complex Fibonacci and Lucas numbers.

Keywords

• Complex numbers
• Fibonacci sequence
• Lucas sequence

2020 Mathematics Subject Classification

• 15A66
• 11B37
• 11Y55

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Manuscript history

• Received: 30 March 2022
• Revised: 26 July 2022
• Accepted: 28 July 2022
• Online First: 29 July 2022