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Percutaneous left atrial appendage closure following catheter ablation therapy of atrial fibrillation: outcomes stratified by bleeding risk - a sub-analysis of the OPTION study. [PDF]
EuropacePhillips KP +14 more
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On the Properties of Balancing and Lucas-Balancing $p$-Numbers
Iranian Journal of Mathematical Sciences and Informatics, 2022 Summary: The main goal of this paper is to develop a new generalization of balancing and Lucas-balancing sequences namely balancing and Lucas-balancing \(p\)-numbers and derive several identities related to them. Some combinatorial forms of these numbers are also presented.
Behera, Adikanda, Ray, Prasanta Kumar
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Factoriangular numbers in balancing and Lucas-balancing sequence
Boletin De La Sociedad Matematica Mexicana, 2020The 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 +2 more
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Balancing and Lucas-balancing numbers which are concatenation of three repdigits
Boletin De La Sociedad Matematica Mexicana, 2023Let \((B_n)_{n\geq 0}\) 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.
Jhon Jairo Bravo Grijalba +1 more
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Brousseau’s Reciprocal Sums Involving Balancing and Lucas-Balancing Numbers
The Journal of the Indian Mathematical Society, 2022In 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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Exact Divisibility by Powers of the Balancing and Lucas-Balancing Numbers
The Fibonacci Quarterly, 2021Asim Patra
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Diophantine equations concerning balancing and Lucas balancing numbers
Archiv Der Mathematik, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Sudhansu Sekhar Rout, Pallab Kanti Dey
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