A combinatorial interpretation of the Perrin sequence

Vieira, Renata P. M.; Spreafico, Elen V. P.; Alves, Francisco R. V.; Catarino, Paula M. M. C.

doi:10.47974/JDMSC-1851

Open Access Research Article

A combinatorial interpretation of the Perrin sequence

^*Renata P. M. VieiraCorresponding authorre.passosm@gmail.comPostgraduate Program in Education of the Northeast Education Network(RENOEN), Universidade Federal do Ceará - Campus da UFC, Rua Campus do PiciFederal University of CearaPici, Fortaleza - CE, BrazilView full profile → , Elen V. P. Spreaficoelen.spreafico@ufms.brDepartament of Mathematics, Universidade Federal de Mato Grosso do SulPioneiros, 79070-900, BrazilView full profile → , Francisco R. V. Alvesfregis@gmxDepartment of MathematicsFederal Institute of Science and Technology Education of the State of CearáCeara, 60040-531, BrazilView full profile → , Paula M. M. C. Catarinopcatarino23@gmailDepartment of MathematicsUniversity of Trás-os-Montes and Alto DouroVila Real, 5001-801, PortugalView full profile →

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pp. 2289–2300Vol. 27Issue 8December 2024DOI: 10.47974/JDMSC-1851 Crossmark XML

Received:: 08 Feb 2023
Published Online:: 18 Dec 2024
Article type:: Research Article
Language:: EN
Article no.:: JDMSC-1851
Pages:: 2289–2300

Abstract

This study focuses on exploring a combinatorial interpretation for the Perrin sequence, with the goal of making a meaningful contribution to the field of Mathematics education. In view of studies focused on the History of Mathematics containing the teaching of recurring numerical sequences present in textbooks, there is an interest in carrying out a combinatorial approach for a sequence regarded as akin to the Fibonacci numbers, which is the Perrin sequence. In this way, we have the definition of Perrin’s bracelets, investigating Perrin’s combinatorial model. Finally, combinatorial interpretations for the Perrin sequence extensions are discussed, generalizing the Perrin combinatorial model.

Keywords

Combinatorics Mathematics teaching Perrin sequence

Subject Classifications

11B3711B3911B75

References

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