Douglas Catulio Santos
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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 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: 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: 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: Os números suavemente ondulantes generalizados
Os números suavemente ondulantes generalizados Open
In this article, for a fixed base d >= 2, we present and analyze some properties associated with the class of smoothly undulating numbers of the form [ab_n]_d, which we will call NSOG. We provide Binet's Formula for every NSOG. In particul…
View article: A note on repunit number sequence
A note on repunit number sequence Open
In this paper, we investigate the classical identities of the repunit sequence with integer indices in light of the properties of Horadan-type sequences. We highlight particularly the Tagiuri-Vajda Identity and Gelin-Cesàro Identity. Addit…
View article: Peculiarities of smoothly undulating number
Peculiarities of smoothly undulating number Open
This notes presents results related to divisibility or multiplicity between two numbers in the class of integers called smoothly undulating numbers of the type uz[n]. The main result is to characterize and display types of divisors of some…