A NOTE OF THE COMBINATORIAL INTERPRETATION OF THE PERRIN AND TETRARRIN SEQUENCE

Author:

VİEİRA Renata1ORCID,PEREİRA SPREAFİCO Elen Viviani2ORCID,ALVES Francisco Regis3ORCID,CRUZ CATARİNO Paula Maria Machado4ORCID

Affiliation:

1. Federal University of Ceara

2. Federal University of Mato Grosso do Sul

3. Federal Institute of Science and Technology Education of the State of Ceara

4. University of Trás-os-Montes and Alto Douro

Abstract

The present study carries out an investigation around the Perrin and Tetrarrin numbers, allowing a combinatorial interpretation for these sequences. Furthermore, it is possible to establish a study around the respective polynomial numbers of Perrin and Tetrarrin, using the bracelet method. With this, we have the definition of combinatorial models of these numbers, contributing to the evolution of these sequences with their respective combinatorial approaches. As a conclusion, there is a discussion of theorems referring to the combinatorial models of these sequences, allowing the study of the mathematical advancement of these numbers.

Publisher

Journal of Universal Mathematics

Subject

General Medicine

Reference14 articles.

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2. A. T. Benjamin, J. J. Quinn, The Fibonacci numbers-exposed more discretely, Math. Magazine, Vol.76, No.3, pp.182-192 (2003).

3. D. Garth, D. Mills, P. Mitchell, Polynomials Generated by the Fibonacci Sequence.\textbf{Journal of Integer Sequences}, v. 10, p. 1-12, 2007.

4. T. Koshy, Fibonacci and Lucas numbers with applications, Second edition, New York: Wiley-Interscience (2019).

5. E. V. P. Spreafico, Novas identidades envolvendo os numeros de Fibonacci, Lucas e Jacobsthal via ladrilhamentos, Doutorado em Matemática Aplicada, Universidade Estadual de Campinas - IME (2014).

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