Dual Leonardo numbers

Adnan Karataş; Adnan Karataş

doi:10.3934/math.20231560

AIMS Mathematics

2023, Volume 8, Issue 12: 30527-30536. doi: 10.3934/math.20231560

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Research article

Dual Leonardo numbers

Adnan Karataş ^,

Department of Mathematics, Faculty of Sciences, Pamukkale University, Denizli, Turkey

Received: 01 September 2023 Revised: 01 November 2023 Accepted: 07 November 2023 Published: 10 November 2023
MSC : 11B39, 11R52

This paper introduced the concept of dual Leonardo numbers to generalize the earlier studies in harmony and establish key formulas, including the Binet formula and the generating function. Both were employed to obtain specific elements from the sequence. Moreover, we presented a range of identities that provided deeper insights into the relationships within this numerical family, such as the Cassini and d'Ocagne identities, along with various summation formulas.
- Leonardo numbers,
- Fibonacci numbers,
- dual numbers,
- identities,
- summation formulas
Citation: Adnan Karataş. Dual Leonardo numbers[J]. AIMS Mathematics, 2023, 8(12): 30527-30536. doi: 10.3934/math.20231560

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Abstract

This paper introduced the concept of dual Leonardo numbers to generalize the earlier studies in harmony and establish key formulas, including the Binet formula and the generating function. Both were employed to obtain specific elements from the sequence. Moreover, we presented a range of identities that provided deeper insights into the relationships within this numerical family, such as the Cassini and d'Ocagne identities, along with various summation formulas.

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