On the Non-Newtonian Padovan and Non-Newtonian Perrin Numbers

Abstract

In this work, we introduce a novel version of Padovan and Perrin numbers which we refer to as non-Newtonian Padovan and non-Newtonian Perrin numbers. Furthermore, we examine about a number of their properties. Additionally, we provide a variety of identities and formulas involving these new kinds, including the Binet-like formulas, the generating functions, the partial sum formulas, and the binomial sum formulas.

Keywords

• Non-Newtonian calculus
• Padovan numbers
• Binet formula
• generating functions
• binomial sum

Newtonian Olmayan Padovan ve Newtonian Olmayan Perrin Sayıları Hakkında

Abstract

Bu çalışmada Newtonian olmayan Padovan ve Newtonian olmayan Perrin sayıları olarak adlandırdığımız Padovan ve Perrin sayılarının yeni bir versiyonunu tanıtıyoruz. Ayrıca bunların bazı özelliklerini de inceliyoruz. Ek olarak, Binet benzeri formüller, üreteç fonksiyonları, kısmi toplam formülleri ve binom toplam formülleri de dahil olmak üzere bu yeni türleri içeren çeşitli özdeşlikler ve formüller sağlıyoruz.

Keywords

• Newtonyen olmayan hesap
• Padovan sayıları
• Binet formülü
• üreteç fonksiyonları
• binom toplamı

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