Results 61 to 70 of about 137 (85)

Generalization of the Distance Fibonacci Sequences

Axioms
In this study, we introduced a generalization of distance Fibonacci sequences and investigate some of its basic properties. We then proposed a generalization of distance Fibonacci sequences for negative integers and investigated some basic properties ...
Nur Şeyma Yilmaz, Andrej Włoch, Engin Özkan   +2 more
doaj   +1 more source

Weighted sum of the sixth powers of Horadam numbers [PDF]

Notes on Number Theory and Discrete Mathematics
Ohtsuka and Nakamura found simple formulas for Σⁿⱼ₌₁Fⱼ⁶ and Σⁿⱼ₌₁Lⱼ⁶, where Fₖ and Lₖ are the k-th Fibonacci and Lucas numbers, respectively. In this note we extend their results to a general second order sequence by deriving a formula for Σⁿⱼ₌₁(-1/q³ ...
Kunle Adegoke, Chiachen Hsu, Olawanle Layeni   +2 more
doaj   +1 more source

Generalized Identities Involving Common Factors of Generalized Fibonacci, Jacobsthal and Jacobsthal-Lucas Numbers

International Journal of Analysis and Applications, 2013
In this paper, we present generalized identities involving common factors of generalized Fibonacci, Jacobsthal and jacobsthal-Lucas numbers. Binet’s formula will employ to obtain the identities.
Yashwant K. Panwar, Bijendra Singh, V. K. Gupta   +2 more
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New Properties and Matrix Representations on Higher-Order Generalized Fibonacci Quaternions with q-Integer Components

Axioms
In this paper, by using q-integers and higher-order generalized Fibonacci numbers, we define the higher-order generalized Fibonacci quaternions with q-integer components. We give some special cases of these newly established quaternions.
Can Kızılateş, Wei-Shih Du, Nazlıhan Terzioğlu, Ren-Chuen Chen   +3 more
doaj   +1 more source

On Generalized Metallic Leonardo Numbers: Silver, Bronze, and Copper Cases

Universal Journal of Mathematics and Applications
In this article, we discuss three new extensions of the Leonardo numbers in a generalized way, which we call the generalized Silver, Bronze, and Copper Leonardo numbers that converge to the Silver, Bronze, and Copper ratios, unifying existing metallic ...
Munesh Kumari, Kalika Prasad, Mritunjay Kumar Singh   +2 more
doaj   +1 more source

On (k1A1, k2A2, k3A3)-Edge Colourings in Graphs and Generalized Jacobsthal Numbers

Annales Mathematicae Silesianae
In this paper we introduce a new kind of generalized Jacobsthal numbers in a distance sense. We give the identities and matrix representations for them and their connections with the Fibonacci and the Pell numbers. We also describe the interpretations of
Piejko Krzysztof, Trojnar-Spelina Lucyna
doaj   +1 more source

Simson Identity of Generalized m-step Fibonacci Numbers [PDF]

International Journal of Advances in Applied Mathematics and Mechanics, 2019
Yüksel Soykan
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Generalized Cassini identities via the generalized Fibonacci fundamental system. Applications

Indian Journal of Pure and Applied Mathematics, 2023
Elen Viviani Pereira Spreafico
exaly  

Generalized k-order Fibonacci and Lucas hybrid numbers

Journal of Information and Optimization Sciences, 2021
Mustafa Asci, Suleyman Aydınyüz
exaly  

Fibonacci Generalized Quaternions

Advances in Applied Clifford Algebras, 2014
Hidayet Huda Kosal, Murat Tosun, Mahmut Akyigit   +2 more
exaly