Results 1 to 10 of about 105,007 (237)

On some identities for the DGC Leonardo sequence [PDF]

Notes on Number Theory and Discrete Mathematics
In this study, we examine the Leonardo sequence with dual-generalized complex (DGC) coefficients for 𝔭∈ℝ. Firstly, we express some summation formulas related to the DGC Fibonacci, DGC Lucas, and DGC Leonardo sequences.
Çiğdem Zeynep Yılmaz, Gülsüm Yeliz Saçlı   +1 more
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Generalized Bronze Leonardo sequence [PDF]

Notes on Number Theory and Discrete Mathematics
In this study, we define the Bronze Leonardo, Bronze Leonardo–Lucas, and Modified Bronze Leonardo sequences, and some terms of these sequences are given. Then, we give special summation formulas, special generating functions, etc.
Engin Özkan, Hakan Akkuş
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Periods of Leonardo Sequences and Bivariate Gaussian Leonardo Polynomials

Düzce Üniversitesi Bilim ve Teknoloji Dergisi
In this study, we investigate the periodic characteristics of Leonardo, Leonardo-Lucas, and Gaussian Leonardo sequences, presenting our findings through lemmas and theorems.
Selime Beyza Özçevik, Abdullah Dertli
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A note on a bivariate Leonardo sequence [PDF]

Notes on Number Theory and Discrete Mathematics
Recently, quite a few generalizations of Leonardo numbers have emerged in the literature. In this short note, we propose a new bivariate extension and provide its generating function.
Carlos M. da Fonseca, Anthony G. Shannon
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A New Generalization of Leonardo Sequences: Biperiodic Leonardo Sequence

Journal of Mathematics
In this study, we define a new type of number sequence called biperiodic Leonardo sequence by the recurrence relation Lena,b=aLen−1+Len−2+1 (for even n) and Lena,b=bLen−1+Len−2+1 (for odd n) with the initial conditions Le0a,b=Le1a,b=1.
Hasan Gökbaş
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On New Banach Sequence Spaces Involving Leonardo Numbers and the Associated Mapping Ideal

Journal of Function Spaces, 2022
In the present study, we have constructed new Banach sequence spaces ℓpL,c0L,cL, and ℓ∞L, where L=lv,k is a regular matrix defined by lv,k=lk/lv+2−v+2, 0≤k≤v,0, k>v, for all v,k=0,1,2,⋯, where l=lk is a sequence of Leonardo numbers.
Taja Yaying, Bipan Hazarika, O. M. Kalthum S. K. Mohamed, Awad A. Bakery   +3 more
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The First Study of Mersenne--Leonardo Sequence

Communications in Advanced Mathematical Sciences
In this study, we introduce a new class of numbers, referred to as Modified Mersenne--Leonardo numbers. The aim of this paper is to define the Modified Mersenne--Leonardo sequence and investigate some of its properties, including the recurrence relation,
Paula Maria Machado Cruz Catarino, Eudes Antonio Costa   +1 more
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On the Leonardo Sequence via Pascal-Type Triangles

Journal of Mathematics
In this study, we discussed the Leonardo number sequence, which has been studied recently and caught more attention. We used Pascal and Hosoya-like triangles to make it easier to examine the basic properties of these numbers.
Serpil Halıcı, Sule Curuk
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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, Peter J.-S. Shiue, Shen C. Huang   +2 more
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On the Hyperbolic Leonardo and Hyperbolic Francois Quaternions

Journal of New Theory, 2023
In this paper, we present a new definition, referred to as the Francois sequence, related to the Lucas-like form of the Leonardo sequence. We also introduce the hyperbolic Leonardo and hyperbolic Francois quaternions.
Paula Maria Machado Cruz Catarino, Orhan Dışkaya, Hamza Menken   +2 more
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