Results 21 to 30 of about 1,995,314 (144)

On Balancing and Lucas-balancing Quaternions [PDF]

, 2021
summary:The aim of this article is to investigate two new classes of quaternions, namely, balancing and Lucas-balancing quaternions that are based on balancing and Lucas-balancing numbers, respectively. Further, some identities including Binet's formulas,
Patel, Bijan Kumar, Ray, Prasanta Kumar
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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

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
doaj  

Two generalizations of dual-complex Lucas-balancing numbers

Acta Universitatis Sapientiae, Mathematica, 2022
AbstractIn this paper, we study two generalizations of dual-complex Lucas-balancing numbers: dual-complex k-Lucas balancing numbers and dual-complex k-Lucas-balancing numbers. We give some of their properties, among others the Binet formula, Catalan, Cassini, d’Ocagne identities.
Bród Dorota, Szynal-Liana Anetta, Włoch Iwona   +2 more
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Mersenne-Horadam identities using generating functions

Karpatsʹkì Matematičnì Publìkacìï, 2020
The main object of the present paper is to reveal connections between Mersenne numbers $M_n=2^n-1$ and generalized Fibonacci (i.e., Horadam) numbers $w_n$ defined by a second order linear recurrence $w_n=pw_{n-1}+qw_{n-2}$, $n\geq 2$, with $w_0=a$ and ...
R. Frontczak, T.P. Goy
doaj   +1 more source

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   +3 more sources

Sum formulas involving powers of balancing and Lucas-balancing numbers – II [PDF]

Notes on Number Theory and Discrete Mathematics, 2019
Summary: In this article, we obtain the closed form expressions for different types of summation formulas involving certain powers of balancing and Lucas-balancing numbers using the telescoping summation formula.
Rayaguru, S. G., Panda, G. K.
openaire   +2 more sources

Some Congruences for Balancing and Lucas-Balancing Numbers and Their Applications

Integers, 2014
See the abstract in the attached pdf.
openaire   +4 more sources

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
doaj   +1 more source

Lucas balancing numbers [PDF]

, 2006
summary:A positive $n$ is called a balancing number if \[1+2+\cdots +(n-1)=(n+1)+(n+2)+\cdots +(n+r).\] We prove that there is no balancing number which is a term of the Lucas ...
Liptai, Kálmán
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