Results 211 to 220 of about 1,424 (225)

Factoriangular numbers in balancing and Lucas-balancing sequence

Boletín de la Sociedad Matemática Mexicana, 2020
The balancing numbers \(\{B_n\}_{n\ge 0}\) have initial terms \(B_0=0,~B_1=1\) and satisfy the recurrence \(B_{n+2}=6B_{n+1}-B_n\) for all \(n\ge 0\). The Lucas-balancing numbers \(\{C_n\}_{n\ge 0}\) have initial terms \(C_0=1,~C_1=3\) and satisfy the same recurrence relation as the balancing numbers.
Sai Gopal Rayaguru, Japhet Odjoumani, Gopal Krishna Panda   +2 more
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Exact Divisibility by Powers of the Balancing and Lucas-Balancing Numbers

The Fibonacci Quarterly, 2021
Asim Patra, G. K. Panda, Tammatada Khemaratchatakumthorn   +2 more
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Diophantine equations concerning balancing and Lucas balancing numbers

Archiv der Mathematik, 2016
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Dey, Pallab Kanti, Rout, Sudhansu Sekhar
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Balancing and Lucas-balancing Numbers Expressible as Sums of Two Repdigits

2021
See the abstract in the attached pdf.
Rayaguru, Sai Gopal, Panda, Gopal Krishna   +1 more
openaire   +2 more sources

INCOMPLETE BALANCING AND LUCAS-BALANCING NUMBERS

2018
The aim of this article is to establish some combinatorial expressions of balancing and Lucas-balancing numbers and investigate some of their properties.
Patel, Bijan Kumar, Irmak, Nurettin, Ray, Prasanta Kumar   +2 more
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Balancing and Lucas-Balancing hybrid numbers and some identities

Journal of Information and Optimization Sciences
In this paper, we introduce Balancing and Lucas-Balancing hybrid numbers. We examine some identities of Balancing and Lucas-Balancing hybrid numbers. We give some basic definitions and properties related to them. In addition, we find Binet’s Formula, Cassini’s identity, Catalan’s identity, d’Ocagne identity, generating functions, exponential generating
Mine Uysal, Engin Özkan
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Octonions and hyperbolic octonions with the k-balancing and k-Lucas balancing numbers

The Journal of Analysis
In this paper, the authors defined the \(k\)-balancing and \(k\)-Lucas balancing octonions and hyperbolic octonions. For \(n\geq 0\), the \(n^{th}\) \(k\)-balancing octonions \(\{B\mathbb{Q}_{k,n}\}\) and the \(n^{th}\) \(k\)-Lucas balancing octonions \(\{C\mathbb{Q}_{k,n}\}\) are defined \[ B\mathbb{Q} _{k,n}=B_{k,n}e_{0}+B_{k,n+1}e_{1}+B_{k,n+2}e_{2}+
Kalika Prasad, Munesh Kumari, Jagmohan Tanti   +2 more
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Certain identities involving \(k\)-balancing and \(k\)-Lucas-balancing numbers via matrices

2023
Summary: Matrix methods are useful to derive several identities for balancing numbers and their related sequences. In this article, two matrices with arithmetic indices, namely \[X_a=\begin{pmatrix} 2C_{k,\alpha} & -1 \\ 1 & 0\end{pmatrix}\text{and} \; Y_a= \begin{pmatrix} C_{k,\alpha} & C_{k,\alpha}-1 \\ 1 & C_{k,\alpha}\end{pmatrix}\] are used to ...
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New Hybrid Numbers with Balancing and Lucas-Balancing Number Components

2023
Nurkan, Semra, Sıddıka Özkaldı Karakuş, Turan, Murat, Ilkay Güven   +3 more
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Nonlinear identities and Diophantine equations involving balancing-like and Lucas-balancing-like numbers

, 2022
Asim Patra, Claudio Pita-Ruiz, Bijan Kumar Patel   +2 more
openalex   +1 more source