Os números híbridos de Leonardo
DOI:
https://doi.org/10.5902/2179460X63773Keywords:
Números híbridos, sequência de Leonardo, número híbrido de Leonardo, identidades.Abstract
No presente trabalho apresentamos um estudo sobre a hibridização da sequência de Leonardo, a partir dos resultados obtidos sobre
esta sequência apresentado por Catarino (2019) e sobre o conjunto dos números híbridos, apresentado por Özdemir (2018). Ao
longo do texto discutimos a hibridização da sequência de Leonardo apresentando definições, teoremas, propriedades, proposições
e identidades com o intuito de apresentar novos resultados relacionados a sequência de Leonardo. E ainda, apresentaremos, uma relação entre os números híbridos de Leonardo com os números híbridos de Fibonacci e, a partir desta relação, exibiremos três identidades clássicas vinculadas a esta sequência híbrida de Leonardo, que são as identidades de: Catalan, Cassini e d’Ocagne.
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Alves, F. R. V., Vieira, R. P. M. (2019). The newton fractal’s Leonardo sequence study with the google colab. International
Electronic Journal of Mathematics Education, 15(2), em0575.
Alves, F. R. V., Catarino, P. M. M. C., Vieira, R. P. M., Mangueira, M. C. d. S. (2020). Teaching recurrent sequences in Brazil
using historical facts and graphical illustrations. Acta Didactica Napocensia, 13(1), 87–104.
Catarino, P. (2019). On k-Pell hybrid numbers. Journal of Discrete Mathematical Sciences and Cryptography, 22(1), 83–89.
Catarino, P., Vasco, P., Borges, A., Campos, H., Aires, A. (2014). Sums, products and identities involving k-Fibonacci and k-Lucas
sequences. JP Journal of Algebra, Number Theory and Applications, 32(1), 63.
Catarino, P. M., Borges, A. (2019). On Leonardo numbers. Acta Mathematica Universitatis Comenianae, 89(1), 75–86.
Cerda-Morales, G. (2018). Investigation of generalized hybrid Fibonacci numbers and their properties. arXiv preprint ar-
Xiv:180602231.
Koshy, T. (2001). Fibonacci and Lucas Numbers with Applications, vol 1. New York: Wileyand Sons publications.
Mangueira, M. C. d. S., Alves, F. R. V., Catarino, P. M. M. C. (2020a). Números híbridos de Mersenne. CQD – Revista Eletrônica Paulista de Matemática, 18, 1–11.
Mangueira, M. C. d. S., Vieira, R. P. M., Alves, F. R. V., Catarino, P. M. M. C. (2020b). The hybrid numbers of Padovan and some
identities. Em: Annales Mathematicae Silesianae, Sciendo, vol 34, pp. 256–267
.
Mangueira, M. C. S., Alves, F. R. V. (2020). Números híbridos de Fibonacci e Pell. Revista Thema, 17(3), 831–842.
Özdemir, M. (2018). Introduction to hybrid numbers. Advances in Applied Clifford Algebras, 28(1), 11.
Shannon, A. (2019). A note on generalized Leonardo numbers. Note on Number Theory and Discrete Mathematics, 25(3), 97–101.
Szynal-Liana, A. (2018). The Horadam hybrid numbers. Discussiones Mathematicae-General Algebra and Applications, 38(1), 91–98.
Szynal-Liana, A., Włoch, I. (2019). On Jacobsthal and Jacobsthal-Lucas hybrid numbers. Em: Annales Mathematicae Silesianae,
Sciendo, vol 33, pp. 276–283.
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.
Vieira, R. P. M., dos Santos Mangueira, M. C., Alves, F. R. V., Catarino, P. M. M. C. (2020). The matrix form of Leonardo’s
numbers. Ciência e Natura, 42, 1–13.
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