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Balancing and Lucas-balancing Numbers Expressible as Sums of Two Repdigits
2021See the abstract in the attached pdf.
Rayaguru, Sai Gopal +1 more
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INCOMPLETE BALANCING AND LUCAS-BALANCING NUMBERS
2018The 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 +2 more
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Balancing and Lucas-Balancing hybrid numbers and some identities
Journal of Information and Optimization SciencesIn 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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Spinor algebra of k-balancing and k-Lucas-balancing numbers
Journal of Algebra and Its ApplicationsIn this paper, we introduce and study a spinor algebra of [Formula: see text]-balancing numbers referred to as the [Formula: see text]-balancing and [Formula: see text]-Lucas-balancing spinors. First, we give [Formula: see text]-balancing quaternions and their some algebraic properties.
Kalika Prasad +3 more
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Some Congruences for Balancing and Lucas-Balancing Numbers and Their Applications
2014See the abstract in the attached pdf.
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On the Properties of Lucas-Balancing Numbers by Matrix Method
Sigmae, 2014Balancing numbers n and balancers r are originally dened as the solution of the Diophantine equation 1 + 2 + ... + (n - 1) = (n + 1) + (n + 2) + ... + (n + r). If n is a balancing number, then 8n^2 +1 is a perfect square. Further, If n is a balancing number then the positive square root of 8n^2 + 1 is called a Lucas-balancing number.
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Certain identities involving \(k\)-balancing and \(k\)-Lucas-balancing numbers via matrices
2023Summary: 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
2023Nurkan, Semra +3 more
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