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Journals / Sigma Mühendislik ve Fen Bilimleri Dergisi / 2026 / Volume: 42 Issue: 5

Some approximations and identities from special sequences for the vertices of suborbital graphs

İbrahim Gökcan(Faculty of Arts and Sciences, Artvin Çoruh University, Artvin, 08010, Türkiye)0000-0002-6933-8494
Ali Hikmet Değer(Department of Mathematics, Karadeniz Technical University, Trabzon, 61080, Türkiye)0000-0003-0764-715X
Ümmügülsün Çağlayan(Department of Mathematics, Karadeniz Technical University, Trabzon, 61080, Türkiye)0000-0002-5870-6802
Pages
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Publication Date
2024-10-04
DOI
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AI Summary & Key Takeaways

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

Then, we provide new identities and approximations regarding Fibonacci, Lucas, Pell, and Pell-Lucas numbers.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, we investigate the vertices arising from the action of a suborbital graph, in terms of continued fractions, matrix, and recurrence relations.
📊
Key Findings & Data:Using the approximation of Fibo-nacci sequence by the Binet formula, we demonstrate that the vertices of the suborbital graph are related to Lucas numbers.
💡
Conclusion & Impact:Then, we provide new identities and approximations regarding Fibonacci, Lucas, Pell, and Pell-Lucas numbers.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Continued Fraction · Generalized Fibonacci Numbers · Modular Group

Abstract

In this study, we investigate the vertices arising from the action of a suborbital graph, in terms of continued fractions, matrix, and recurrence relations. Using the approximation of Fibo-nacci sequence by the Binet formula, we demonstrate that the vertices of the suborbital graph are related to Lucas numbers. Then, we provide new identities and approximations regarding Fibonacci, Lucas, Pell, and Pell-Lucas numbers.

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Cite This Article

Gökcan, İ., Değer, A. H., Çağlayan, Ü. (2024). Some approximations and identities from special sequences for the vertices of suborbital graphs. Sigma Mühendislik ve Fen Bilimleri Dergisi, Volume: 42 Issue: 5. https://ajindex.com/articles/1344443

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