On the Mersenne sequence

From Binet’s formula of Mersenne sequence we get some properties for this sequence. Mersenne, Jacobsthal and Jacobsthal-Lucas sequences are considered in order to achieve some relations between them, sums and certain products involving terms of these sequences. We also present some results with matrices involving Mersenne numbers such as the generating matrix, tridiagonal matrices and circulant type matrices

Some combinatorial matrices and their LU-decomposition

CITATION: Prodinger, H. 2020. Some combinatorial matrices and their LU-decomposition. Special Matrices, 8:61–67, doi:10.1515/spma-2020-0007.The original publication is available at https://www.degruyter.comThree combinatorial matrices were considered and their LU-decompositions were found. This is typically done by (creative) guessing, and the proofs are more or less routine calculations.Publisher's versio

Horadam sequences: A survey update and extension.

We give an update on work relating to Horadam sequences that are generated by a general linear recurrence formula of order two. This article extends a first ever survey published in early 2013 in this Bulletin, and includes coverage of a new research area opened up in recent times.N/

An investigation of the bivariate complex Fibonacci polynomials supported in didactic engineering: an application of theory of didactics situations (TSD)

A research cut will be presented in the Academic Master of the Programa de Pós-Graduação em Ensino de Ciências e Matemática (PGECM) of the Instituto Federal de Educação, Ciência e Tecnologia do Ceará (IFCE). This research used Didactic Engineering with a focus on the Theory of Didactic Situations, evidencing epistemological, cognitive and didactic elements articulated among themselves. This made it possible to mobilize the student’s intuitive thinking towards inferential reasoning during the study of the Bivariate Complex Fibonacci Polynomials. Moreover, it had the purpose of inserting an epistemological conception in the teaching of History of Mathematics, considering that the research was applied in the course of Degree in Mathematics in the discipline of History of Mathematics