Some Properties of Generalized Jacobsthal-Like Sequences

Year 2024, Volume: 14 Issue: 2, 92 - 96, 23.07.2024

Can Murat Dikmen , Kübra Karataş Selam

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.

Keywords

Generalized Jacobsthal-Like sequences, Jacobsthal sequence, Jacobsthal-Lucas sequences

Project Number

2

Genelleştirilmiş Jacobsthal-Benzeri Dizilerin Bazı Özellikleri

Abstract

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.

Keywords

Genelleştirilmiş Jacobsthal-benzeri diziler, Jacobsthal dizisi, Jacobsthal-Lucas dizileri

Project Number

2

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