Results 1 to 10 of about 2,031,724 (254)

Periods of Leonardo Sequences and Bivariate Gaussian Leonardo Polynomials [PDF]

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.
Abdullah Dertli, Beyza Özçevik
exaly   +7 more sources

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
doaj   +6 more sources

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
doaj   +4 more sources

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
exaly   +3 more sources

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,
Eudes A Costa, Paula Catarino
exaly   +5 more sources

Hybrid Quaternions of Leonardo

Trends in Computational and Applied Mathematics, 2022
In this article, we intend to investigate the Leonardo sequence presenting the hybrid Leonardo quaternions. To explore Hybrid Quaternions of Leonardo, the priori, sequence of Leonardo, quaternions and hybrid numbers were presented.
Francisco Regis Alves
exaly   +3 more sources

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
doaj   +2 more sources

A New Family of Number Sequences: Leonardo-Alwyn Numbers

Armenian Journal of Mathematics, 2023
In this study, we define a new type of number sequence called Leonardo-Alwyn sequence. We obtain the Binet formula, generating function and some relations for these numbers. Moreover, we give the matrix representation of the Leonardo-Alwyn numbers.
exaly   +2 more sources

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
doaj   +2 more sources

A Note on Bi-Periodic Leonardo Sequence

Armenian Journal of Mathematics
In this work, we define a new generalization of the Leonardo sequence by the recurrence relation $GLe_n=aGLe_{n-1}+GLe_{n-2}+a$ (for even $n$) and $GLe_n=bGLe_{n-1}+GLe_{n-2}+b$ (for odd $n$) with the initial conditions $GLe_0=2a-1$ and $GLe_1=2ab-1$, where $a$ and $b$ are real nonzero numbers.
Elen Viviani Pereira Spreafico, Paula Catarino   +1 more
exaly   +3 more sources