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2020
In this paper, we introduce a new generalization of the balancing numbers which we call bi-periodic balancing numbers ...
Taşcı, Dursun, Sevgi, Emre
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In this paper, we introduce a new generalization of the balancing numbers which we call bi-periodic balancing numbers ...
Taşcı, Dursun, Sevgi, Emre
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2021
In this work, we determine the general terms of k-almost balancing numbers and k-almost Lucas-balancing numbers of first and second type in terms of balancing and Lucas-balancing numbers for some integer k >= 1.
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In this work, we determine the general terms of k-almost balancing numbers and k-almost Lucas-balancing numbers of first and second type in terms of balancing and Lucas-balancing numbers for some integer k >= 1.
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On t-Balancers, t-Balancing Numbers and Lucas t-Balancing Numbers
2021Aydın, Samet, Tekcan, Ahmet
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Aequationes mathematicae
\textit{L. C. Hsu} and \textit{P. J. S. Shiue} [Adv. Appl. Math. 20, No. 3, 366--384 (1998; Zbl 0913.05006)] introduced a far-reaching generalization of Stirling numbers, \(S(n,k;\alpha,\beta,r)\), and they gave eleven known combinatorial sequences as specializations. \textit{B. Bényi} et al. [Integers 22, Paper A79, 28 p.
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\textit{L. C. Hsu} and \textit{P. J. S. Shiue} [Adv. Appl. Math. 20, No. 3, 366--384 (1998; Zbl 0913.05006)] introduced a far-reaching generalization of Stirling numbers, \(S(n,k;\alpha,\beta,r)\), and they gave eleven known combinatorial sequences as specializations. \textit{B. Bényi} et al. [Integers 22, Paper A79, 28 p.
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2017
In this work, we consider some algebraic properties of k-balancing numbers. We deduce some formulas for the greatest common divisor of k-balancing numbers, divisibility properties of k-balancing numbers, sums of k-balancing numbers and simple continued fraction expansion of k-balancing numbers.
TEKCAN, AHMET, Ozkoc, Arzu
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In this work, we consider some algebraic properties of k-balancing numbers. We deduce some formulas for the greatest common divisor of k-balancing numbers, divisibility properties of k-balancing numbers, sums of k-balancing numbers and simple continued fraction expansion of k-balancing numbers.
TEKCAN, AHMET, Ozkoc, Arzu
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Properties of balancing, cobalancing and generalized balancing numbers
2010Summary: A positive integer \(n\) is called a balancing number if \[ 1+2+\dots+(n-1) = (n+1)+(n+2)+\dots +(n+r) \] for some positive integer \(r\). Several authors investigated balancing numbers and their various generalizations. The goal of this paper is to survey some interesting properties and results on balancing, cobalancing and all types of ...
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