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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 55 Issue: 5

Some properties of the coupled Leonardo sequence

Elis G. Mesquita(Federal University of Tocantins)0000-0003-2385-4108
F. R. V. Alves(Federal Institute of Education, Science and Technology of Ceará)0000-0003-3710-1561
Fernando Carvalho(Federal University of Tocantins)0000-0001-6639-0716
Eudes Antonio Costa(Federal University of Tocantins)0000-0001-6684-9961
Pages
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Publication Date
2026-10-28
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The ordinary generating function is obtained, and the partial sums are examined.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we introduce a new Leonardo-type sequence, which we call the coupled Leonardo sequence.
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Key Findings & Data:This sequence is defined by a non-homogeneous second-order recurrence involving two real parameters and a real-valued coupling function, with fixed initial terms.
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Conclusion & Impact:The ordinary generating function is obtained, and the partial sums are examined.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Leonardo Numbers · Generalized Leonardo Numbers · Horadam Numbers

Abstract

In this paper, we introduce a new Leonardo-type sequence, which we call the coupled Leonardo sequence. This sequence is defined by a non-homogeneous second-order recurrence involving two real parameters and a real-valued coupling function, with fixed initial terms. The coupling function plays an important role and allows us to propose a new Leonardo-type generalization—originally defined in terms of the Fibonacci numbers—to the setting of an arbitrary Horadam sequence. Under suitable assumptions on the parameters, we introduce three classes of generalizations of the Leonardo sequence corresponding to distinct structural cases. We derive a Binet-type formula and several algebraic properties that allow us to establish relations between the coupled Leonardo sequence and the associated Horadam sequence. The ordinary generating function is obtained, and the partial sums are examined.

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Cite This Article

Mesquita, E. G., Alves, F. R. V., Carvalho, F., Costa, E. A. (2026). Some properties of the coupled Leonardo sequence. Hacettepe Journal of Mathematics and Statistics, Volume: 55 Issue: 5. https://doi.org/10.15672/hujms.1913798

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