Combinatorial approach on the recurrence sequences: An evolutionary historical discussion about numerical sequences and the notion of the board

Francisco Regis Vieira Alves; Paula Maria Machado Cruz Catarino; Renata Passos Machado Vieira; Elen Viviani Pereira Spreafico

doi:10.29333/iejme/14387

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Francisco Regis Vieira Alves ¹ ^* , Paula Maria Machado Cruz Catarino ² , Renata Passos Machado Vieira ³ , Elen Viviani Pereira Spreafico ⁴

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¹ Federal Institute of Education, Science and Technology of the State of Ceará–IFCE, Fortaleza, Ceará, BRAZIL² University of Trás-os-Montes and Alto Douro, Vila Real, PORTUGAL³ RENOEN/UFC, BRAZIL⁴ Federal University of Mato Grosso do Sul, Campo Grande, BRAZIL^* Corresponding Author

Abstract

The tradition of studies involving the combinatorial approach to recurring numerical sequences has accumulated a few decades of tradition, and several problems continue to attract the interest of mathematicians in several countries. This work specifically discusses the Fibonacci, Pell, and Jacobsthal sequences, focusing on Mersenne sequences. The often-used definition of board involves considering how to fill a specific regular surface -the board- with a limited quantity of regularly shaped tiles. On the other hand, an analogous problem can be generalized and exemplifies current research developments. Finally, the examples covered constitute unexpected ways of exploring visualization and other skills in mathematics teachers’ learning, consequently inspiring them for their teaching context.

Keywords

numerical sequences
combinatorial approach
board and tiles
mathematics teacher education

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

INT ELECT J MATH ED, Volume 19, Issue 2, May 2024, Article No: em0775

https://doi.org/10.29333/iejme/14387

Publication date: 01 Apr 2024

Online publication date: 22 Mar 2024

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How to cite this article

APA

Alves, F. R. V., Catarino, P. M. M. C., Vieira, R. P. M., & Spreafico, E. V. P. (2024). Combinatorial approach on the recurrence sequences: An evolutionary historical discussion about numerical sequences and the notion of the board. International Electronic Journal of Mathematics Education, 19(2), em0775. https://doi.org/10.29333/iejme/14387

Vancouver

Alves FRV, Catarino PMMC, Vieira RPM, Spreafico EVP. Combinatorial approach on the recurrence sequences: An evolutionary historical discussion about numerical sequences and the notion of the board. INT ELECT J MATH ED. 2024;19(2):em0775. https://doi.org/10.29333/iejme/14387

AMA

Alves FRV, Catarino PMMC, Vieira RPM, Spreafico EVP. Combinatorial approach on the recurrence sequences: An evolutionary historical discussion about numerical sequences and the notion of the board. INT ELECT J MATH ED. 2024;19(2), em0775. https://doi.org/10.29333/iejme/14387

Chicago

Alves, Francisco Regis Vieira, Paula Maria Machado Cruz Catarino, Renata Passos Machado Vieira, and Elen Viviani Pereira Spreafico. "Combinatorial approach on the recurrence sequences: An evolutionary historical discussion about numerical sequences and the notion of the board". International Electronic Journal of Mathematics Education 2024 19 no. 2 (2024): em0775. https://doi.org/10.29333/iejme/14387

Harvard

Alves, F. R. V., Catarino, P. M. M. C., Vieira, R. P. M., and Spreafico, E. V. P. (2024). Combinatorial approach on the recurrence sequences: An evolutionary historical discussion about numerical sequences and the notion of the board. International Electronic Journal of Mathematics Education, 19(2), em0775. https://doi.org/10.29333/iejme/14387

MLA

Alves, Francisco Regis Vieira et al. "Combinatorial approach on the recurrence sequences: An evolutionary historical discussion about numerical sequences and the notion of the board". International Electronic Journal of Mathematics Education, vol. 19, no. 2, 2024, em0775. https://doi.org/10.29333/iejme/14387