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Journals / Karaelmas Fen ve Mühendislik Dergisi / 2026 / Cilt: 14 Sayı: 2

Some Properties of Generalized Jacobsthal-Like Sequences

Can Murat Dikmen(ZONGULDAK BÜLENT ECEVİT ÜNİVERSİTESİ)0000-0002-1837-1139
Kübra Karataş Selam(ZONGULDAK BÜLENT ECEVİT ÜNİVERSİTESİ)0000-0002-6490-440X
Pages
92–96
Publication Date
2024-07-23
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AI Summary & Key Takeaways

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

We also prove some other summation formulas like sum of even and odd indices and alternating sum of generalized Jacobsthal-Like sequences.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this article, using Jacobsthal and Jacobsthal-Lucas sequences, we define generalized Jacobsthal-Like sequences and investigate their algebraic properties like Binet’s formula, generating functions, Simson formula and summation formula.
📊
Key Findings & Data:In this article, using Jacobsthal and Jacobsthal-Lucas sequences, we define generalized Jacobsthal-Like sequences and investigate their algebraic properties like Binet’s formula, generating functions, Simson formula and summation formula.
💡
Conclusion & Impact:We also prove some other summation formulas like sum of even and odd indices and alternating sum of generalized Jacobsthal-Like sequences.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:Genelleştirilmiş Jacobsthal-benzeri diziler · Jacobsthal dizisi · Jacobsthal-Lucas dizileri

Abstract

In this article, using Jacobsthal and Jacobsthal-Lucas sequences, we define generalized Jacobsthal-Like sequences and investigate their algebraic properties like Binet’s formula, generating functions, Simson formula and summation formula. We also prove some other summation formulas like sum of even and odd indices and alternating sum of generalized Jacobsthal-Like sequences.

Özet

Bu makalede Jacobsthal ve Jacobsthal-Lucas dizilerini kullanarak genelleştirilmiş Jacobsthal-Benzeri dizilerini tanımlayıp Binet formülü, üreten fonksiyonlar, Simson formülü ve toplam formülü gibi cebirsel özelliklerini araştırıyoruz. Ayrıca çift ve tek indekslerin toplamı ve genelleştirilmiş Jacobsthal-Benzeri dizilerinin alterne toplamı gibi diğer toplama formüllerini de kanıtlıyoruz.

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Cite This Article

Selam, K. K., Dikmen, C. M. (2024). Some Properties of Generalized Jacobsthal-Like Sequences. Karaelmas Fen ve Mühendislik Dergisi, Cilt: 14 Sayı: 2, 92–96. https://doi.org/10.7212/karaelmasfen.1443277

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References (12)

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