New Features for k-Jacobsthal And k-Jacobsthal-Lucas Sequence

Year 2026, Volume: 9 Issue: 1, 1 - 13, 28.02.2026

Şükran Uygun

https://izlik.org/JA73HK74BE

Abstract

Special integer sequences can be generalized by different many ways. The basic form of these ways is to add a parameter to recurrence relation. From special sequences, k-Jacobsthal, k-Jacobsthal-Lucas sequences are obtained adding a parameter to the recurrence relation of the Jacobsthal and Jacobsthal-Lucas numbers. In literature, there are some papers concerning the properties of k-Jacobsthal and k-Jacobsthal-Lucas sequences. But, we think they are not sufficient, so we aim to study new properties of these generalized sequences. The features related with k-Jacobsthal and k-Jacobsthal-Lucas sequences will be acquired through the Binet formulas, recurrence relations, generating functions of these numbers.

Keywords

Binet formula , Generating function , k-Jacobsthal number , k-Jacobsthal–Lucas number

k-Jacobsthal And k-Jacobsthal-Lucas Dizileri İçin Yeni Özellikler

https://izlik.org/JA73HK74BE

Abstract

Özel tamsayı dizileri birçok farklı yolla genelleştirilebilir. Bu yolların temel biçimi, yineleme bağıntısına bir parametre eklemektir. Özel dizilerden, Jacobsthal ve Jacobsthal-Lucas sayılarının yineleme bağıntısına bir parametre eklenerek k-Jacobsthal ve k-Jacobsthal-Lucas dizileri elde edilir. Literatürde, k-Jacobsthal ve k-Jacobsthal-Lucas dizilerinin özellikleriyle ilgili bazı makaleler bulunmaktadır. Ancak, bunların yeterli olmadığını düşünüyoruz, bu nedenle bu genelleştirilmiş dizilerin yeni özelliklerini incelemeyi amaçlıyoruz. k-Jacobsthal ve k-Jacobsthal-Lucas dizileriyle ilgili özellikler, Binet formülleri, yineleme bağıntıları ve bu sayıların üreteç fonksiyonları aracılığıyla elde edilecektir.

Keywords

Binet formülü , Üreteç fonksiyonu , k-Jacobsthal sayısı , k-Jacobsthal–Lucas sayısı

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