Results 1 to 10 of about 85,197 (264)

A study on the sum of the squares of generalized Balancing numbers: the sum formula $\sum_{k=0}^{n}x^{k}W_{mk+j}^{2}$

Journal of Innovative Applied Mathematics and Computational Sciences, 2021
In this paper, closed forms of the sum formulas $\sum_{k=0}^{n}x^{k}W_{mk+j}^{2}$ for generalized balancing numbers are presented. As special cases, we give sum formulas of balancing, modified Lucas-balancing and Lucas-balancing numbers.
Yüksel Soykan, Erkan Taşdemir, Can Murat Dikmen   +2 more
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On the Partial Finite Alternating Sums of Reciprocals of Balancing and Lucas-Balancing Numbers

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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The Tribonacci-type balancing numbers and their applications [PDF]

Mathematica Moravica, 2023
N this paper, we define the Tribonacci-type balancing numbers via a Diophantine equation with a complex variable and then give their miscellaneous properties. Also, we study the Tribonacci-type balancing sequence modulo m and then obtain some interesting
Hulku Sakıne, Devec Ömür
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Solutions of the Diophantine Equations Br=Js+Jt and Cr=Js+Jt

Journal of Mathematics, 2023
Let Brr≥0, Jrr≥0, and Crr≥0 be the balancing, Jacobsthal, and Lucas balancing numbers, respectively. In this paper, the diophantine equations Br=Js+Jt and Cr=Js+Jt are completely solved.
Ahmed Gaber, Mohiedeen Ahmed
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Polygonal Balancing Numbers I

, 2022
See the abstract in the attached pdf.
Bartz, Jeremiah, Dearden, Bruce, Iiams, Joel   +2 more
openaire   +3 more sources

Simulation Verification of Balancing System Based on Number of Cells

Communications, 2021
This paper deals with the simulation verification of balancing systems with different numbers of batteries. There is a simulation model of the battery with adjustable inputs and a simulation model of flyback converter. These components are interconnected
Marek Šimčák, Matúš Danko
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Almost Gap Balancing Numbers

Integers, 2018
See the abstract in the attached pdf.
Jeremiah Bartz, Bruce Dearden, Joel Iiams   +2 more
openaire   +4 more sources

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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Almost repdigits in balancing and Lucas-balancing sequences [PDF]

Notes on Number Theory and Discrete Mathematics
In this paper, we define the notion of almost repdigit as a positive integer whose digits are all equal except for at most one digit, and we search all terms of the balancing and Lucas-balancing sequences which are almost repdigits.
Manasi K. Sahukar, Hussain Basha
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ON DUAL BICOMPLEX BALANCING AND LUCAS-BALANCING NUMBERS

Journal of Science and Arts, 2023
In this paper, dual bicomplex Balancing and Lucas-Balancing numbers are defined, and some identities analogous to the classic properties of the Fibonacci and Lucas sequences are produced. We give the relationship between these numbers and Pell and Pell-Lucas numbers.
MINE UYSAL, ENGIN ÖZKAN, ANTHONY G. SHANNON   +2 more
openaire   +1 more source