Results 41 to 50 of about 10,886,718 (351)
Sums of Pell/Lucas Polynomials and Fibonacci/Lucas Numbers
Mathematics, 2022 Seven infinite series involving two free variables and central binomial coefficients (in denominators) are explicitly evaluated in closed form. Several identities regarding Pell/Lucas polynomials and Fibonacci/Lucas numbers are presented as consequences.
Dongwei Guo, Wenchang Chu
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A Combinatorial Proof of a Result on Generalized Lucas Polynomials
Demonstratio Mathematica, 2016 We give a combinatorial proof of an elementary property of generalized Lucas polynomials, inspired by [1]. These polynomials in s and t are defined by the recurrence relation 〈n〉 = s〈n-1〉+t〈n-2〉 for n ≥ 2.
Laugier Alexandre, Saikia Manjil P.
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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.
M. Uysal +2 more
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Some new identities of a type of generalized numbers involving four parameters
AIMS Mathematics, 2022 This article deals with a Horadam type of generalized numbers involving four parameters. These numbers generalize several celebrated numbers in the literature such as the generalized Fibonacci, generalized Lucas, Fibonacci, Lucas, Pell, Pell-Lucas ...
Waleed Mohamed Abd-Elhameed +2 more
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Occupational choice, number of entrepreneurs and output: theory and empirical evidence with Spanish data [PDF]
, 2013 This paper extends the (Lucas, Bell J Econ 9:508–523,1978) model of occupational choices by individuals with different skills, beyond the simple options of self-employment or wage-employment, by including a second choice for the self-employed.
AJ Stel van +26 more
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Weighted sum of the sixth powers of Horadam numbers [PDF]
Notes on Number Theory and Discrete MathematicsOhtsuka and Nakamura found simple formulas for Σⁿⱼ₌₁Fⱼ⁶ and Σⁿⱼ₌₁Lⱼ⁶, where Fₖ and Lₖ are the k-th Fibonacci and Lucas numbers, respectively. In this note we extend their results to a general second order sequence by deriving a formula for Σⁿⱼ₌₁(-1/q³ ...
Kunle Adegoke +2 more
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On Bicomplex Jacobsthal-Lucas Numbers
Journal of Mathematical Sciences and Modelling, 2020 In this study we introduced a sequence of bicomplex numbers whose coefficients are chosen from the sequence of Jacobsthal-Lucas numbers. We also present some identities about the known some fundamental identities such as the Cassini's, Catalan's and Vajda's identities.
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The Frobenius Number for Jacobsthal Triples Associated with Number of Solutions
Axioms, 2023 In this paper, we find a formula for the largest integer (p-Frobenius number) such that a linear equation of non-negative integer coefficients composed of a Jacobsthal triplet has at most p representations.
T. Komatsu, C. Pita-Ruiz
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, 2021 {"references": ["1.\tR. Sivaraman, Number Triangles and Metallic Ratios, International Journal of Engineering and Computer Science, Volume 10, Issue 8, pp. 25365 \u2013 25369. 2.\tR. Sivaraman, Generalized Pascal's Triangle and Metallic Ratios, International Journal of Research, Volume 9, Issue 7, pp. 179 \u2013 184. 3.\tR.
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Bilecik Şeyh Edebali Üniversitesi Fen Bilimleri Dergisi, 2022 The present work aims to introduce and study the Gaussian Bronze Lucas number sequence. Firstly, we define Gaussian Bronze Lucas numbers by extending the Bronze Lucas numbers. Then, we find the Binet formula and generating function for this number sequence. We also investigate some sum formulas and matrices related to the Gaussian Bronze Lucas numbers.
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