Results 1 to 10 of about 11,602 (209)

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
doaj   +3 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   +4 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   +2 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

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
doaj   +3 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

The Newton Fractal’s Leonardo Sequence Study with the Google Colab [PDF]

International Electronic Journal of Mathematics Education, 2019
The work deals with the study of the roots of the characteristic polynomial derived from the Leonardo sequence, using the Newton fractal to perform a root search. Thus, Google Colab is used as a computational tool to facilitate this process.
Francisco Régis Vieira Alves, Renata Passos Machado Vieira   +1 more
exaly   +2 more sources

Didactic Engineering to Teach Leonardo Sequence: A Study on a Complexification Process in a Mathematics Teaching Degree Course [PDF]

International Electronic Journal of Mathematics Education, 2021
This paper presents a study based on didactic engineering and the theory of didactical situations on the complexification of the Leonardo sequence, addressing its numbers in a two-dimensional way, with the insertion of the imaginary unit i. This study is an excerpt from a masters’ thesis research done in the postgraduate programme in science and ...
Francisco Régis Vieira Alves, Milena Carolina dos Santos Mangueira, Paula Catarino   +2 more
exaly   +2 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,
Paula Maria Machado Cruz Catarino, Eudes Antonio Costa   +1 more
doaj   +3 more sources

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
doaj   +3 more sources