Results 11 to 20 of about 102,319 (175)
Earthline Journal of Mathematical Sciences, 2022 In this paper, we define and investigate modified p-Leonardo, p-Leonardo-Lucas and p-Leonardo sequences as special cases of the generalized Leonardo sequence. We present Binet's formulas, generating functions, Simson formulas, and the summation formulas for these sequences.
Yüksel Soykan
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Ordered Leonardo Quadruple Numbers [PDF]
Symmetry, 2023 In this paper, we introduce a new quadruple number sequence by means of Leonardo numbers, which we call ordered Leonardo quadruple numbers. We determine the properties of ordered Leonardo quadruple numbers including relations with Leonardo, Fibonacci, and Lucas numbers. Symmetric and antisymmetric properties of Fibonacci numbers are used in the proofs.
Semra Kaya Nurkan, İlkay Arslan Güven
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A new perspective on bicomplex numbers with Leonardo number components
Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics, 2023 In the present paper, the bicomplex Leonardo numbers will be introduced with the use of Leonardo numbers and some important algebraic properties including recurrence relation, generating function, Catalan’s and Cassini’s identities, Binet’s formula, sum formulas will also be obtained.
Murat TURAN +2 more
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Notes on generalized and extended Leonardo numbers [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 This paper both extends and generalizes recently published properties which have been developed by many authors for elements of the Leonardo sequence in the context of second-order recursive sequences.
Anthony G. Shannon +2 more
doaj +2 more sources
, 2023 In this paper, we introduce a new generalization of Leonardo numbers, which are so-called Leonardo $p$-numbers. We investigate some basic properties of these numbers. We also define incomplete Leonardo $p$-numbers which generalize the incomplete Leonardo numbers.
Tan, Elif, Leung, Ho-Hun
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Generalized Horadam-Leonardo Numbers and Polynomials
Asian Journal of Advanced Research and Reports, 2023 In this study, we define and investigate some linear third order polynomials called the generalized Horadam-Leonardo polynomials (with its two special cases, namely), (r, s)-Horadam-Leonardo and (r, s)-Horadam-Leonardo-Lucas polynomials. We give Binet’s formulas, generating functions, Simson formulas, and the sumformulas for these polynomial sequences.
Yüksel Soykan
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GAUSSIAN LEONARDO POLYNOMIALS AND APPLICATIONS OF LEONARDO NUMBERS TO CODING THEORY
Journal of Science and Arts, 2023 In this paper, we firstly introduce the Gaussian Leonardo polynomial sequences {GLe_n (x)}_(n=0)^∞ and we obtain Binet's formula, generating function of this sequence. Moreover, we define the matrix Gl(x) in the form of 3 x 3. Finally, we study on the coding and decoding applications of the Leonardo number by using the Leonardo matrix P.
SELİME BEYZA ÖZÇEVİK +1 more
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On Leonardo Pisano Hybrinomials
Mathematics, 2021 A generalization of complex, dual, and hyperbolic numbers has recently been defined as hybrid numbers. In this study, using the Leonardo Pisano numbers and hybrid numbers we investigate Leonardo Pisano polynomials and hybrinomials.
Ferhat Kürüz +2 more
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Leonardo and hyper-Leonardo numbers via Riordan arrays
Ukrains’kyi Matematychnyi ZhurnalUDC 511 A generalization of the Leonardo numbers is defined and called the hyper-Leonardo numbers. Infinite lower triangular matrices, whose elements are Leonardo and hyper-Leonardo numbers are considered. Then the A - and Z -sequences of these matrices are obtained. Finally, the combinatorial identities between the hyper-Leonardo and Fibonacci
Yasemin Alp, E. Gokcen Kocer
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Hybrinomials related to hyper-Leonardo numbers
Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics, 2023 In this paper, we define hybrinomials related to hyper-Leonardo numbers. We study some of their properties such as the recurrence relation and summation formulas. In addition, we introduce hybrid hyper Leonardo numbers.
Efruz Özlem MERSİN, Mustafa BAHŞİ
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