Shifted Fibonacci Numbers

Yıl 2023, Cilt: 23 Sayı: 6, 1440 - 1444, 28.12.2023

Adnan Karataş

https://doi.org/10.35414/akufemubid.1345862

Öz

Shifted Fibonacci numbers have been examined in the literature in terms of the greatest common divisor, but appropriate definitions and fundamental equations have not been worked on. In this article, we have obtained the Binet formula, which is a fundamental equation used to obtain the necessary element of the shifted Fibonacci number sequence. Additionally, we have obtained many well-known identities such as Cassini, Honsberger, and various other identities for this sequence. Furthermore, summation formulas for shifted Fibonacci numbers have been presented.

Anahtar Kelimeler

Shifted Fibonacci Numbers, Binet Formula, Identities, Summation Formulas

Kaymış Fibonacci Sayıları

Öz

Kaymış Fibonacci sayıları, literatürde, en büyük ortak bölen açısından incelenmiştir, ancak uygun tanım ve temel denklemler çalışılmamıştır. Bu makalede, kaymış Fibonacci sayı dizisinin gerekli elemanını elde etmek için kullanılan ve temel bir formül olan Binet formülünü verdik. Ayrıca, Cassini, Honsberger ve diğer birçok bilinen özdeşlikleri ve bu dizi için çok sayıda farklı özdeşlikler elde edilmiştir. Ayrıca, kaymış Fibonacci sayıları için toplama formülleri sunulmuştur.

Anahtar Kelimeler

Kaymış Fibonacci Sayıları, Binet Formülü, Özdeşlikler, Toplam Formülleri

Kaynakça

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