A New Family of Number Sequences: Leonardo-Alwyn Numbers

Gökbaş, Hasan

doi:10.52737/18291163-2023.15.6-1-13

Cited by 4 publications

(1 citation statement)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Moreover, some identities of Leonardo numbers were obtained in [8]. Recent studies on Leonardo numbers have investigated various generalizations of Leonardo numbers in [9][10][11][12][13][14][15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Some Properties of the Generalized Leonardo Numbers

Alp

2024

Journal of New Theory

View full text Add to dashboard Cite

In this study, various properties of the generalized Leonardo numbers, which are one of the generalizations of Leonardo numbers, have been investigated. Additionally, some identities among the generalized Leonardo numbers have been obtained. Furthermore, some identities between Fibonacci numbers and generalized Leonardo numbers have been provided. In the last part of the study, binomial sums of generalized Leonardo numbers have been derived. The results obtained for generalized Leonardo numbers are reduced to Leonardo numbers.

show abstract

Section: Introductionmentioning

confidence: 99%

Some Properties of the Generalized Leonardo Numbers

Alp

2024

Journal of New Theory

View full text Add to dashboard Cite

show abstract

State of the art on the Leonardo sequence: An evolutionary study of the epistemic-mathematical field

Mangueira,

Alves,

Catarino

et al. 2024

PEDAGOGICAL RES

View full text Add to dashboard Cite

This work is a segment of an ongoing doctoral research in Brazil. The Leonardo numbers and the Leonardo sequence have gained attention from mathematicians and the academic community. Despite being a relatively new sequence within mathematical literature, its discussion has intensified over the past five years, giving rise to other branches, with contributions and associations to other topics in mathematics. Thus, the aim of this study was to construct and present the state of the art of the Leonardo sequence, considering its historical aspects and highlighting works on its evolutionary process in the epistemic-mathematical field, regarding its generalization, complexification, hyper complexification, and combinatorial model during the last five years (2019-2023). The methodology used was a bibliographic study, where the state of the art was carried out through the mapping of publications on the subject. Twenty-four research works related to the key descriptors “Leonardo sequence”, “Leonardo numbers”, “complexification”, “generalization”, “hybrids”, and “combinatorial model” were found, cataloged, and discussed. From the analysis of these studies, it is noted that its development in pure mathematics has advanced to other branches and discoveries, and that, albeit timidly, research on the subject has emerged directed towards the field of education, especially in the initial teacher training and, particularly, in Brazil.

show abstract