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A multi-country mixed method evaluation of the HERA (Healthcare Responding to Domestic Violence and Abuse) intervention: A comparative analysis.

SSM Health Syst
Bacchus LJ, Pereira S, Joudeh N, Kalichman BD, K C S, Siriwardhana P, Silva T, Lucas d'Oliveira AFP, Rishal P, Shrestha S, Schraiber LB, Alkaiyat A, Rajapakse T, Shaheen A, Feder G, Lambert H, Moreno CG, Colombini M, HERA research team.   +18 more
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Factoriangular numbers in balancing and Lucas-balancing sequence

Boletín de la Sociedad Matemática Mexicana, 2020
The balancing numbers \(\{B_n\}_{n\ge 0}\) have initial terms \(B_0=0,~B_1=1\) and satisfy the recurrence \(B_{n+2}=6B_{n+1}-B_n\) for all \(n\ge 0\). The Lucas-balancing numbers \(\{C_n\}_{n\ge 0}\) have initial terms \(C_0=1,~C_1=3\) and satisfy the same recurrence relation as the balancing numbers.
Sai Gopal Rayaguru, Japhet Odjoumani, Gopal Krishna Panda   +2 more
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Diophantine equations concerning balancing and Lucas balancing numbers

Archiv der Mathematik, 2016
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Dey, Pallab Kanti, Rout, Sudhansu Sekhar
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Balancing and Lucas-balancing numbers which are concatenation of three repdigits

Boletín de la Sociedad Matemática Mexicana, 2023
Let \((B_n)_{n\geq 0}\) be sequence A001109 and \((C_n)_{n\geq 0}\) be sequence A001541 in OEIS. Both sequences have the same characteristic polynomial \(x^2-6x+1\). We have \[B_n=\frac{\alpha^n-\beta^n}{4\sqrt{2}}\mbox{ and }C_n=\frac{\alpha^n+\beta^n}{2}\] for all \(n\geq0\), where \(\alpha=3+2\sqrt{2}\) resp.
S. G. Rayaguru, Jhon J. Bravo
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On the Periodicity of Lucas-Balancing Numbers and p-adic Order of Balancing Numbers

Iranian Journal of Science and Technology, Transactions A: Science, 2020
The objective of this article is to study the periodicity of Lucas-balancing numbers modulo any positive integer. Some relations between the periodicity of balancing and Lucas-balancing numbers are also discussed. Further, in this study the p-adic order of balancing numbers is completely characterized .
Takao Komatsu, Bijan Kumar Patel, Prasanta Kumar Ray   +2 more
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Octonions and hyperbolic octonions with the k-balancing and k-Lucas balancing numbers

The Journal of Analysis
In this paper, the authors defined the \(k\)-balancing and \(k\)-Lucas balancing octonions and hyperbolic octonions. For \(n\geq 0\), the \(n^{th}\) \(k\)-balancing octonions \(\{B\mathbb{Q}_{k,n}\}\) and the \(n^{th}\) \(k\)-Lucas balancing octonions \(\{C\mathbb{Q}_{k,n}\}\) are defined \[ B\mathbb{Q} _{k,n}=B_{k,n}e_{0}+B_{k,n+1}e_{1}+B_{k,n+2}e_{2}+
Kalika Prasad, Munesh Kumari, Jagmohan Tanti   +2 more
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Brousseau’s Reciprocal Sums Involving Balancing and Lucas-Balancing Numbers

The Journal of the Indian Mathematical Society, 2022
In this paper, we derive the closed form expressions for the finite and infinite sums with summands having products of balancing and Lucas-balancing numbers in the denominator. We present some generalized Brousseau’s sums for balancing and Lucas-balancing numbers.
Rayaguru, S. G., Panda, G. K.
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Positive Integer Solutions of Some Diophantine Equations Involving Lucas-Balancing Numbers

The Fibonacci Quarterly, 2020
Asim Patra, G. K. Panda
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