31 citations · 118 across the 26 of their papers we have counts for
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On the third-order Horadam and geometric mean sequences
Gamaliel Cerda-Morales
This paper, in considering aspects of the geometric mean sequence, offers new results connecting generalized Tribonacci and third-order Horadam numbers which are established and th…
On the third-order Horadam matrix sequences
Gamaliel Cerda-Morales
In this paper, we first give new generalizations for third-order Horadam and generalized Tribonacci sequence…
The Gelin-Cesàro identity in some third-order Jacobsthal sequences
Gamaliel Cerda-Morales
In this paper, we deal with two families of third-order Jacobsthal sequences. The first family consists of generalizations of the Jacobsthal sequence. We show that the Gelin-Cesàro…
Third-order Jacobsthal Generalized Quaternions
Gamaliel Cerda-Morales
In this paper, the third-order Jacobsthal generalized quaternions are introduced. We use the well-known identities related to the third-order Jacobsthal and third-order Jacobsthal-…
Bicomplex Third-order Jacobsthal Quaternions
Gamaliel Cerda
The aim of this work is to consider the bicomplex third-order Jacobsthal quaternions and to present some properties involving this sequence, including the Binet-style formulae and…
The unifying formula for all Tribonacci-type octonions sequences and their properties
Gamaliel Cerda-Morales
Various families of octonion number sequences (such as Fibonacci octonion, Pell octonion and Jacobsthal octonion) have been established by a number of authors in many different way…
A Three-by-Three matrix representation of a generalized Tribonacci sequence
Gamaliel Cerda-Morales
The Tribonacci sequence is a well-known example of third order recurrence sequence, which belongs to a particular class of recursive sequences. In this article, other generalized T…
Quadratic Approximation of Generalized Tribonacci Sequences
Gamaliel Cerda-Morales
In this paper, we give quadratic approximation of generalized Tribonacci sequence defined by Eq. (\ref{eq:7}) and use this result to give the matrix form of th…
On the third-order Jacobsthal and third-order Jacobsthal-Lucas sequences and their matrix representations
Gamaliel Cerda-Morales
In this paper, we first give new generalizations for third-order Jacobsthal and third-order Jacobsthal-Lucas …
Investigation of Generalized Hybrid Fibonacci Numbers and Their Properties
Gamaliel Cerda-Morales
In \cite{Oz}, M. Özdemir defined a new non-commutative number system called hybrid numbers. In this paper, we define the hybrid Fibonacci and Lucas numbers. This number system can…
Identities involving Narayana numbers
Gamaliel Cerda-Morales
Narayana's cows problem is a problem similar to the Fibonacci's rabbit problem. We define the numbers which are the solutions of this problem as Narayana's cows numbers. Narayana's…
Dual Third-order Jacobsthal Quaternions
Gamaliel Cerda-Morales
In 2016, Yüce and Torunbalcı Aydın \cite{Yuc-Tor} defined dual Fibonacci quaternions. In this paper, we defined the dual third-order Jacobsthal quaternions and dual third-order Jac…