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

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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, 2024, Volume 19, Issue 2, Article No: em0775

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

Publication date: 01 Apr 2024

Online publication date: 22 Mar 2024

Article Views: 395

Article Downloads: 318

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