Results 31 to 40 of about 2,078,136 (239)
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 +2 more
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Repdigits as Products of Consecutive Balancing or Lucas-Balancing Numbers
The Fibonacci Quarterly, 2018 Repdigits are natural numbers formed by the repetition of a single digit. In this paper, we explore the presence of repdigits in the product of consecutive balancing or Lucas-balancing numbers.
Rayaguru, Sai Gopal +1 more
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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 +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
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Balancing and Lucas-balancing Numbers Expressible as Sums of Two Repdigits
, 2021 See the abstract in the attached pdf.
Rayaguru, Sai Gopal +1 more
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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.
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Combinatorial sums associated with balancing and Lucas-balancing polynomials [PDF]
, 2020 The aim of the paper is to use some identities involving binomial coefficients to derive new combinatorial identities for balancing and Lucas-balancing polynomials.
Goy, Taras, Frontczak, Robert
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Some Congruences for Balancing and Lucas-Balancing Numbers and Their Applications
Integers, 2014 See the abstract in the attached pdf.
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On Balancing and Lucas-balancing Quaternions
, 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 +3 more
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Almost repdigits in balancing and Lucas-balancing sequences [PDF]
Notes on Number Theory and Discrete MathematicsIn 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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