A note on the Tetrarrin sequence

Authors

DOI:

https://doi.org/10.14393/BEJOM-v5-2024-69801

Keywords:

Extension, Perrin sequence, Tetrarrin sequence

Abstract

This study explores an extension of the Perrin sequence, defining the Tetrarrin sequence. Thus, we investigated Tetrarrin numbers and their mathematical relationships, allowing a deeper understanding of Perrin numbers. In this context, we analyze Binet?s formula, the matrix form, among other theorems, making it possible to obtain the terms of this new sequence using different methods. It is important to highlight that the Tetrarrin sequence is of higher order and derived from the Perrin sequence. For future work, we intend to integrate this content with other areas of study, in addition to using tools and software that enable the visualization of the mathematical properties of this sequence in a more intuitive and accessible way.

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Author Biographies

Renata Passos Machado Vieira, Universidade Federal do Ceará

PhD student in Teaching at the Northeast Education Network (RENOEN-UFC Pole). Professor at the Education Department of the State of Ceará - Brazil. Postgraduate Program in Teaching at the Northeast Education Network (RENOEN-UFC Pole); CNPQ Research Group; Funcap scholarship holder.

Francisco Regis Vieira Alves, Instituto Federal de Educação Ciência e Tecnologia do Ceará

PhD with emphasis on teaching Mathematics - UFC. Full Professor at the Federal Institute of Education, Science and Technology of the state of Ceará - IFCE. Professor and Coordinator of the Postgraduate Program in Teaching at the Northeast Education Network (RENOEN-Polo IFCE). Member of the CNQP research group. CNPq Research Productivity Scholarship - Level 2.

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

PhD in Mathematics - University of Essex Department of Mathematical Sciences. Associate Professor at UTAD (University of Trás-os-Montes and Alto Douro) with habilitation. Researcher at the CMAT-UTAD Research Center - CMAT Pole of the University of Minho and also Researcher at the CIDTFF Research Center - Research Center “Didactics and Technology in Trainer Training. Currently Member of the General Council of UTAD.

References

PERRIN, M. R. Sur une methode nouvelle de notation des enclenchements, Paris: [S. n.], 1905.

SANTOS, A. A. dos. Engenharia Didatica sobre o estudo da formula de Binet como modelo de generalizacao e extensao da sequencia de Fibonacci, 2017. 163 f. Dissertacao (Mestrado em Ensino de Ciencias e Matematica) - Programa de Mestrado Academico em Ensino de Ciencias e Matematica, Instituto Federal de Educacao, Ciencia e Tecnologia do Estado do Ceara, Fortaleza, 2017.

SLOANE, N. J. A. An on-line version of the encyclopedia of integer sequences, 1964. Url: https://oeis.org/.

VIEIRA, R. P. M. and ALVES, F. R. V. Sequences of Tridovan and their identities, Notes on Number Theory and Discrete Mathematics, v. 25, n. 3, (2019), 185-197.

WADDILL, M. E. The Tetranacci sequence and generalizations, The Fibonacci Quarterly, v. 30, n. 1, (1992), 9-19.

TAN, B., WEN, Z. Some properties of the Tribonacci sequence, European Journal of Combinatorics, v. 28, n. 6, (2007), 1703-1719.

GOMES, C. A. and OLIVEIRA, O. R. B. de. O teorema de Cayley-Hamilton. IME-USP-Oswaldo Rio Branco de Oliveira, (2019), 1-11.

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Published

2024-08-20

How to Cite

VIEIRA, R. P. M.; ALVES, F. R. V.; CATARINO, P. M. M. C. A note on the Tetrarrin sequence. BRAZILIAN ELECTRONIC JOURNAL OF MATHEMATICS, Uberlândia, v. 5, p. 1–11, 2024. DOI: 10.14393/BEJOM-v5-2024-69801. Disponível em: https://seer.ufu.br/index.php/BEJOM/article/view/69801. Acesso em: 31 aug. 2024.

Issue

Vol. 5 (2024): Brazilian Electronic Journal of Mathematics

Section

Articles - Pure Mathematics

License

Copyright (c) 2024 Renata Passos Machado Vieira, Francisco Regis Vieira Alves, Paula Maria Machado Cruz Catarino

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