The Matrix Form of Leonardo’s Numbers

Authors

DOI:

https://doi.org/10.5902/2179460X41839

Keywords:

Generalization, generating matrix, leonardo’s numbers

Abstract

In this work we will investigate the generating matrices for the positive integers of the Leonardo sequence, as well as some inherent properties of these matrices. In order to perform the process of generalizing the matrix form of Leonardo’s numbers, the extension to the field of non-positive integers is performed, in which the study of these matrices is unpublished in this research. The matrix form relates the matrices to the Leonardo numbers, and by raising these matrices to nth power, we obtain some new relations of this sequence, thus knowing their respective terms.

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Author Biographies

Renata Passos Machado Vieira, IFCE (Instituto de Educação, Ciência e Tecnologia do Estado do Ceará)

Educação Matemática

Matemática

Milena Carolina dos Santos Mangueira, Instituto Federal do Ceará, Fortaleza, CE

Mestranda em Ensino de Ciências e Matemática. Departamento de Matemática

Francisco Regis Vieira Alves, Instituto Federal do Ceará, Fortaleza, CE

Professor Doutor e Coordenador do Mestrado Acadêmico em Ensino de Ciências e Matemática. Departamento de Matemática

Paula Maria Machado Cruz Catarino, Universidade de Trás-os-Montes e Alto Douro, Vila Real, Portugal

Professora Pós-doutora. Departamento de Matemática

References

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Vieira, R. P. M., Alves, F. R. V., Catarino, P. M. M. C. (2019). Relações bidimensionais e identidades da sequência de leonardo. Revista Sergipana de Matemática e Educação Matemática, 4(2), 156–173.

Published

2020-12-23

How to Cite

Vieira, R. P. M., Mangueira, M. C. dos S., Alves, F. R. V., & Catarino, P. M. M. C. (2020). The Matrix Form of Leonardo’s Numbers. Ciência E Natura, 42, e100. https://doi.org/10.5902/2179460X41839

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