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INCOMPLETE BALANCING AND LUCAS-BALANCING NUMBERS [PDF]
, 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 +2 more
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Generalized Balancing and Balancing-Lucas numbers
Proyecciones (Antofagasta)In this paper, we introduce a generalization of Balancing and Balancing-Lucas numbers. We describe some of their properties also we give the related matrix representation and divisibility properties.
Al-Zoubi, Hasan, Al-Kateeb, Ala'a
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On the Partial Finite Alternating Sums of Reciprocals of Balancing and Lucas-Balancing Numbers [PDF]
Discussiones Mathematicae - General Algebra and Applications, 2020 In this note, the finite alternating sums of reciprocals of balancing and Lucas-balancing numbers are considered and several identities involving these sums are deduced.
Dutta Utkal Keshari, Ray Prasanta Kumar
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On the properties of k-balancing and k-Lucas-balancing numbers [PDF]
Acta et Commentationes Universitatis Tartuensis de Mathematica, 2017 The k-Lucas-balancing numbers are obtained from a special sequence of squares of k-balancing numbers in a natural form. In this paper, we will study some properties of k-Lucas-balancing numbers and establish relationship between these numbers and k-balancing numbers.
Prasanta Kumar Ray, Ray, Prasanta Kumar
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On Balancing Quaternions and Lucas-Balancing Quaternions
Discussiones Mathematicae - General Algebra and Applications, 2021 In this paper we define and study balancing quaternions and Lucas-balancing quaternions. We give the generating functions, matrix generators and Binet formulas for these numbers. Moreover, the well-known properties e.g. Catalan, d’ Ocagne identities have
Bród Dorota
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A New Identity Involving Balancing Polynomials and Balancing Numbers [PDF]
Symmetry, 2019 In this paper, a second-order nonlinear recursive sequence M ( h , i ) is studied. By using this sequence, the properties of the power series, and the combinatorial methods, some interesting symmetry identities of the structural properties of balancing numbers and balancing polynomials are deduced.
Yuanyuan Meng
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Bidimensional extensions of balancing and Lucas-balancing numbers [PDF]
Journal of Discrete Mathematical Sciences & CryptographyIn this article bidimensional extensions of balancing and Lucas-balancing numbers are introduced, as well as some properties of these new bidimensional sequences.
Chimpanzo, J. +3 more
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On arithmetic functions of balancing and Lucas-balancing numbers [PDF]
Mathematical Communications, 2019 For any integers $n\geq1$ and $k\geq0,$ let $\phi(n)$ and $\sigma_{k}(n)$ denote the Euler phi function and the sum of the $k$-th powers of the divisors of $n$, respectively. In this article, the solutions to some Diophantine equations about these functions of balancing and Lucas-balancing numbers are discussed.
Dutta, Utkal Keshari +1 more
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The Balancing Number and Generalized Balancing Number of Some Graph Classes
The Electronic Journal of Combinatorics, 2023 Given a graph $G$, a 2-coloring of the edges of $K_n$ is said to contain a balanced copy of $G$ if we can find a copy of $G$ such that half of its edges is in each color class. If there exists an integer $k$ such that, for $n$ sufficiently large, every 2-coloring of $K_n$ with more than $k$ edges in each color contains a balanced copy of $G$, then we ...
Antoine Dailly +3 more
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Classes of gap balancing numbers [PDF]
Rocky Mountain Journal of Mathematics, 2021 14 ...
Bartz, Jeremiah +2 more
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