Jacobsthal ve Jacobsthal Lucas sayıları ve uygulamaları
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Dosyalar
Tarih
2008-07-02
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Selçuk Üniversitesi Fen Bilimleri Enstitüsü
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
Bu çalışmada, Horadam tarafından tanımlanmış olan Jacobsthal ve Jacobsthal Lucas sayılarının verilen özelliklerine ek olarak bazı özellikler elde edildi. Jacobsthal sayılarının bölünebilme özellikleri verildi. Jacobsthal dizisinin matris uygulamaları için, Jacobsthal F ve M matrislerini tanımlandıktan sonra Jacobsthal sayılarının matris gösterimi elde edildi. Ek olarak, Jacobsthal Lucas E ve R matrislerini tanımlayıp, bu iki dizinin de matrisler ile bağlantısı verildi. Ayrıca, Fibonacci ve Jacobsthal dizilerinin bir genelleştirilmesi olarak k-Jacobsthal dizileri, Lucas ve Jacobsthal Lucas dizilerinin bir genelleştirilmesi olarak da k-Jacobsthal Lucas dizilerinin tanımları ve özellikleri verildi.
In this study, we have found some properties of Jacobsthal and Jacobsthal Lucas numbers, which are defined by Horadam, in addition to properties of Jacobsthal and Jacobsthal Lucas numbers given A. F. Horadam. We have obtained divisibility property of Jacobsthal numbers. We have defined Jacobsthal F and M matrices for matrix application of Jacobsthal sequences and have obtained matrix representation of Jacobsthal numbers. In addition, we have given relation between both sequences with matrices, after we have defined Jacobsthal Lucas E and R matrices. Also, we have given properties and definition of k-Jacobsthal sequences that is defined as a generalization of Fibonacci and Jacobsthal sequences, and have given properties and definition of k-Jacobsthal Lucas sequence that is defined as generalization of the Lucas and Jacobsthal Lucas sequences.
In this study, we have found some properties of Jacobsthal and Jacobsthal Lucas numbers, which are defined by Horadam, in addition to properties of Jacobsthal and Jacobsthal Lucas numbers given A. F. Horadam. We have obtained divisibility property of Jacobsthal numbers. We have defined Jacobsthal F and M matrices for matrix application of Jacobsthal sequences and have obtained matrix representation of Jacobsthal numbers. In addition, we have given relation between both sequences with matrices, after we have defined Jacobsthal Lucas E and R matrices. Also, we have given properties and definition of k-Jacobsthal sequences that is defined as a generalization of Fibonacci and Jacobsthal sequences, and have given properties and definition of k-Jacobsthal Lucas sequence that is defined as generalization of the Lucas and Jacobsthal Lucas sequences.
Açıklama
Anahtar Kelimeler
Fibonacci dizileri, Fibonacci sequences, Jacobsthal ve Jacobsthal Lucas sayıları, Genelleştirilmiş Fibonacci dizileri, Genelleştirilmiş Lucas dizileri, Matris metodu, Jacobsthal and Jacobsthal Lucas numbers, Generalized Fibonacci sequences, Generalized Lucas sequences, Matrix method
Kaynak
WoS Q Değeri
Scopus Q Değeri
Cilt
Sayı
Künye
Köken, F. (2008). Jacobsthal ve Jacobsthal Lucas sayıları ve uygulamaları. Selçuk Üniversitesi, Yayımlanmış yüksek lisans tezi, Konya.
