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Journals / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2026 / Volume: 73 Issue: 3

An extended framework for bihyperbolic generalized Tribonacci numbers

Nurten Gürses(yıldız teknik üniversitesi)0000-0001-8407-854X
Zehra İşbilir(DUZCE UNIVERSITY)0000-0001-5414-5887
Pages
—
Publication Date
2024-09-27
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AI Summary & Key Takeaways

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

Then, we examine several properties by taking two special cases and including some illustrative numerical examples.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The aim of this article is to identify and analyze a new type special number system which is called bihyperbolic generalized Tribonacci numbers (BGTN for short).
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Key Findings & Data:For this purpose, we give both classical and several new properties such as; recurrence relation, Binet formula, generating function, exponential generating function, summation formulae, matrix formula, and special determinant equations of BGTN .
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Conclusion & Impact:Then, we examine several properties by taking two special cases and including some illustrative numerical examples.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Generalized Tribonacci numbers · bihyperbolic numbers · bihyperbolic generalized Tribonacci numbers

Abstract

The aim of this article is to identify and analyze a new type special number system which is called bihyperbolic generalized Tribonacci numbers (BGTN for short). For this purpose, we give both classical and several new properties such as; recurrence relation, Binet formula, generating function, exponential generating function, summation formulae, matrix formula, and special determinant equations of BGTN . Also, the system of BGTN is quite a big family and includes several type special cases with respect to initial values and $r,~ s, ~t$ values, we give the subfamilies and special cases of it. In addition to these, we construct some numerical algorithms including recurrence relation and special two types determinant equations related to calculating the terms of this new type special number system. Then, we examine several properties by taking two special cases and including some illustrative numerical examples.

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Cite This Article

Gürses, N., İşbilir, Z. (2024). An extended framework for bihyperbolic generalized Tribonacci numbers. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 73 Issue: 3. https://doi.org/10.31801/cfsuasmas.1378136

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