Paula Catarino
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View article: On Tricomplex Horadam Numbers: A New Class of Horadam Sequences
On Tricomplex Horadam Numbers: A New Class of Horadam Sequences Open
This study introduces an innovative approach to Horadam sequences. The aim of this paper is to investigate the Tricomplex Horadam sequence and its properties. It begins with the tricomplex ring T and key results related to Horadam-type seq…
View article: On Matrices with Bidimensional Fibonacci Numbers
On Matrices with Bidimensional Fibonacci Numbers Open
In this paper, the bidimensional extensions of the Fibonacci numbers are explored, along with a detailed examination of their properties, characteristics, and some identities. We introduce and study the matrices with bidimensional Fibonacc…
View article: Visualization and properties of boards and tiles: The case of the Padovan or Cordonier sequence
Visualization and properties of boards and tiles: The case of the Padovan or Cordonier sequence Open
The study of recurring numerical sequences usually involves a restricted context of circulation and communication of new ideas and abstract mathematical properties. On the other hand, authors of the history of mathematics books tend to emp…
View article: The first study of the Jacobsthal-Mulatu Numbers
The first study of the Jacobsthal-Mulatu Numbers Open
The aim of this study is to find a sequence of Jacobsthal-type numbers, which we will denote by {JMn}n≥0 and name as the sequence of Jacobsthal-Mulatu, such that each term of the Jacobsthal-Lucas sequence, denoted by {jn}n≥0, is an average…
View article: Abordagem prática para a utilização do software octave: transferência de calor por condução unidimensional em regime transiente
Abordagem prática para a utilização do software octave: transferência de calor por condução unidimensional em regime transiente Open
This study investigates the use of Octave software as a tool to support the learning of concepts of heat transfer by one-dimensional conduction in a transient regime. This mixed-method research proposes and analyzes teaching plans for teac…
View article: A Note on Hybrid Numbers with Generalized Hybrid k-Pell Numbers as Coefficients
A Note on Hybrid Numbers with Generalized Hybrid k-Pell Numbers as Coefficients Open
In this study, we define a new generalization of the hybrid $k$-Pell sequence consisting of hybrid numbers with generalized hybrid $k$-Pell numbers as coefficients. We establish some algebraic properties and also the Binet formula, generat…
View article: On t-Dimensional Gersenne Sequences and Their Symmetry Properties
On t-Dimensional Gersenne Sequences and Their Symmetry Properties Open
In this paper, we introduce a new class of sequences of integers called t-dimensional Gersenne sequences, with 2≤t<∞, which extends the classical Mersenne-type sequences into higher dimensions by incorporating complex and hyper-complex str…
View article: A note on the generalized bi-periodic Lucas-balancing numbers
A note on the generalized bi-periodic Lucas-balancing numbers Open
In this study, we introduce a new class of integers called the sequence of generalized bi-periodic Lucas-balancing numbers, which extends the well-known sequence of Lucas-balancing numbers. We present several fundamental properties, includ…
View article: On tridimensional Lucas-balancing numbers and some properties
On tridimensional Lucas-balancing numbers and some properties Open
In this article, we introduce the tridimensional version of the Lucas-balancing numbers based on the unidimensional version, and we also study some of their properties and sum identities.
View article: On Gersenne Sequence: A Study of One Family in the Horadam-Type Sequence
On Gersenne Sequence: A Study of One Family in the Horadam-Type Sequence Open
This study introduces an innovative approach to Mersenne-type numbers. This paper introduces a new class of numbers, which we call Gersenne numbers. The aim of this paper is to define the Gersenne sequence and to investigate some of their …
View article: The First Study of Mersenne--Leonardo Sequence
The First Study of Mersenne--Leonardo Sequence Open
In this study, we introduce a new class of numbers, referred to as Modified Mersenne--Leonardo numbers. The aim of this paper is to define the Modified Mersenne--Leonardo sequence and investigate some of its properties, including the recur…
View article: A Brief Study on the k-Dimensional Repunit Sequence
A Brief Study on the k-Dimensional Repunit Sequence Open
In this paper, we aim to introduce and investigate the bidimensional, tridimensional and k-dimensional extension of Repunit numbers, with a particular focus on their recurrence relations, key properties, and various sum identities.
View article: Using GeoGebra as a tool for teaching the Padovan board and tiling
Using GeoGebra as a tool for teaching the Padovan board and tiling Open
This study is part of ongoing doctoral research investigating the teaching of Padovan's combinatorial approach and the scarcity of works on this topic. The objective is to propose an approach to explore combinatorial identities with the he…
View article: Some Tridiagonal Matrix of the Repunit Sequence
Some Tridiagonal Matrix of the Repunit Sequence Open
This paper explores the connection between tridiagonal matrices and the repunit sequence, which is a type of Horadam sequence, and aims to establish new representations of repunit sequences using distinct tridiagonal matrices and their det…
View article: A Study of the Symmetry of the Tricomplex Repunit Sequence with Repunit Sequence
A Study of the Symmetry of the Tricomplex Repunit Sequence with Repunit Sequence Open
In this paper, we introduce a new family of sequences related to Horadam-type sequences. Specifically, we consider the repunit sequence {rn}n≥0, which is defined by the initial terms r0=0 and r1=1 and follows the Horadam recurrence relatio…
View article: Tricomplex Fibonacci Numbers: A New Family of Fibonacci-Type Sequences
Tricomplex Fibonacci Numbers: A New Family of Fibonacci-Type Sequences Open
In this paper, we define a novel family of arithmetic sequences associated with the Fibonacci numbers. Consider the ordinary Fibonacci sequence {fn}n∈N0 having initial terms f0=0, and f1=1 and recurrence relation fn=fn−1+fn−2(n≥2). In many…
View article: On the Incomplete Edouard and Incomplete Edouard–Lucas Numbers
On the Incomplete Edouard and Incomplete Edouard–Lucas Numbers Open
This study introduces two new sequences: the incomplete Edouard and the incomplete Edouard–Lucas numbers. In addition, we establish some of the properties, identities, and recurrence relations of these sequences. The relations of these new…
View article: On a Matrix Formulation of the Sequence of Bi-Periodic Fibonacci Numbers
On a Matrix Formulation of the Sequence of Bi-Periodic Fibonacci Numbers Open
In this study, we investigate some new properties of the sequence of bi-periodic Fibonacci numbers with arbitrary initial conditions, through an approach that combines the matrix aspect and the fundamental Fibonacci system. Indeed, by cons…
View article: On the Leonardo quaternions sequence
On the Leonardo quaternions sequence Open
In the present work, a new sequence of quaternions related to the Leonardo numbers -- named the Leonardo quaternions sequence -- is defined and studied. Binet's formula and certain sum and binomial-sum identities, some of which derived fro…
View article: Extensão da sequência de Leonardo: Tetra-Leonardo, Penta-Leonardo e Hexa-Leonardo
Extensão da sequência de Leonardo: Tetra-Leonardo, Penta-Leonardo e Hexa-Leonardo Open
This research presents an expansion of the Leonardo sequence, a recurrence associated with a characteristic polynomial of degree 3, now encompassing sequences of recurrences associated with a characteristic polynomial of degree 4 (Tetra-Le…
View article: A correction on the paper "A Note on Bi-Periodic Leonardo Sequence''
A correction on the paper "A Note on Bi-Periodic Leonardo Sequence'' Open
The generating function in Theorem 3 of our work [1] was computed incorrectly. We provide the new version of Theorem 3 including the corrections to be made in its proof. The authors are grateful to Carlos M. Da Fonseca [2] for identifying …
View article: A Note on Bi-Periodic Leonardo Sequence
A Note on Bi-Periodic Leonardo Sequence Open
In this work, we define a new generalization of the Leonardo sequence by the recurrence relation $GLe_n=aGLe_{n-1}+GLe_{n-2}+a$ (for even $n$) and $GLe_n=bGLe_{n-1}+GLe_{n-2}+b$ (for odd $n$) with the initial conditions $GLe_0=2a-1$ and $G…
View article: A note on hybrid hyper Leonardo numbers
A note on hybrid hyper Leonardo numbers Open
Recently, many studies have been devoted to extending particular sets of integers to other special sets, such as complex, dual, hyperbolic, and hybrid numbers. In this study, we define a new generalization of the Leonardo sequence consisti…
View article: State of the art on the Leonardo sequence: An evolutionary study of the epistemic-mathematical field
State of the art on the Leonardo sequence: An evolutionary study of the epistemic-mathematical field Open
This work is a segment of an ongoing doctoral research in Brazil. The Leonardo numbers and the Leonardo sequence have gained attention from mathematicians and the academic community. Despite being a relatively new sequence within mathemati…
View article: A didactic engineering for the study of the Padovan’s combinatory model
A didactic engineering for the study of the Padovan’s combinatory model Open
Considering the content of history of mathematics textbooks, it’s evident that their emphasis is primarily on the illustrative aspects of recurring numerical sequences, with a particular focus on the Fibonacci sequence. Unfortunately, this…
View article: Some Identities and Generating Functions for Bidimensional Balancing and Cobalancing Sequences
Some Identities and Generating Functions for Bidimensional Balancing and Cobalancing Sequences Open
This article studies the bidimensional versions of four number sequences: balancing, Lucas-balancing, Lucas-cobalancing and cobalancing. Some of the identities and generating functions were presented.
View article: Combinatorial approach on the recurrence sequences: An evolutionary historical discussion about numerical sequences and the notion of the board
Combinatorial approach on the recurrence sequences: An evolutionary historical discussion about numerical sequences and the notion of the board Open
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 w…
View article: ON GENERALIZED ORESME NUMBERS AND THE FIBONACCI FUNDAMENTAL SYSTEM
ON GENERALIZED ORESME NUMBERS AND THE FIBONACCI FUNDAMENTAL SYSTEM Open
In this work we study the generalized Oresme numbers using the algebraic properties of the Fibonacci fundamental system associated with this sequence. We explicitly describe the closed connection between the sequences of the Fibonacci fund…
View article: A NOTE OF THE COMBINATORIAL INTERPRETATION OF THE PERRIN AND TETRARRIN SEQUENCE
A NOTE OF THE COMBINATORIAL INTERPRETATION OF THE PERRIN AND TETRARRIN SEQUENCE Open
The present study carries out an investigation around the Perrin and Tetrarrin numbers, allowing a combinatorial interpretation for these sequences. Furthermore, it is possible to establish a study around the respective polynomial numbers …