The Hybrid Numbers of Padovan and Some Identities
Annales Mathematicae Silesianae, 2020 In this article, we will define Padovan’s hybrid numbers, based on the new noncommutative numbering system studied by Özdemir ([7]). Such a system that is a set involving complex, hyperbolic and dual numbers.
Mangueira Milena Carolina dos Santos +3 more
doaj +1 more source
BAZI FARK DENKLEMLERİNİN AYARLANMIŞ JACOBSTHAL-PADOVAN SAYILARI İLE İLİŞKİLİ TAM ÇÖZÜMLERİ [PDF]
, 2022 In this paper, we obtain the form of the solutions of some rational difference equations via adjusted Jacobsthal-Padovan numbers. We find a relation between the exact solutions and the adjusted Jacobsthal-Padovan numbers.
Melih GÖCEN
core +1 more source
sequence of the hyperbolic k-Padovan quaternions
Malaya Journal of Matematik, 2023 This work introduces the hyperbolic k-Padovan quaternion sequence, performing the process of complexification of linear and recurrent sequences, more specifically of the generalized Padovan sequence. In this sense, there is the study of some properties around this sequence, deepening the investigative mathematical study of these numbers.
Renata Passos Machado Vieira +2 more
openaire +1 more source
Binomial Transforms of the Padovan and Perrin Matrix Sequences [PDF]
Abstract and Applied Analysis, 2013 We apply the binomial transforms to Padovan and Perrin matrix sequences. Also, the Binet formulas, summations, and generating functions of these transforms are found by recurrence relations. Finally, we illustrate the relations between these transforms by deriving new formulas.
Yilmaz, Nazmiye, Taskara, Necati
openaire +3 more sources
The (s; t)-Padovan Quaternions Matrix Sequence [PDF]
, 2020 In this paper, we will introduce the (s; t)-Padovan quaternionsmatrix sequence. Starting the studies based on the generalization of thePadovan quaternion coefficients in relation to their recurrence, their matrixsequence is then defined.
Renata Passos Machado Vieira; Department of Mathematics, Federal Institute of Education, Science and Technology of the State of Ceara +2 more
core
An extension of Lucas identity via Pascal's triangle [PDF]
, 2021 The Fibonacci sequence can be obtained by drawing diagonals in a Pascal’s triangle, and from this, we can obtain the Lucas identity. An investigation on the behavior of certain kinds of other diagonals inside a Pascal’s triangle identifies a new family ...
Giuseppina ANATRIELLO +3 more
core +3 more sources
A Didactic Engineering in the Research Process of the Generalization of the Padovan Sequence: An Experience in a Pre-Service Teacher Training Course [PDF]
, 2020 Background: Obstacles are found during the epistemological construction of mathematical concepts research, aiming to contribute to the Didactics of Mathematics through a study of Padovan sequence.
Vieira, Renata Passos Machado +3 more
core +1 more source
Here we find the Padovan and Perrin numbers that are concatenations of two terms of the other sequence. We also find the intersection between these ternary sequences. [PDF]
, 2023 Here we find the Padovan and Perrin numbers that are concatenations of two terms of the other sequence. We also find the intersection between these ternary sequences.
Bravo, Eric Fernando
core +3 more sources
Some infinite series summations involving linear recurrence relations of order 2 and 3 [PDF]
Notes on Number Theory and Discrete MathematicsThis paper extends known results of second and third order recursive sequences through extensive formulations of properties of the roots of their characteristic equations, some are old but most are new. They are applied to novel studies of Σₙ₌ₒ^∞ aₘₙ/10ⁿ⁺
Anthony G. Shannon +4 more
doaj +1 more source
Padovan and Perrin numbers as products of two generalized Lucas numbers [PDF]
, 2023 summary:Let $P_m$ and $E_m$ be the $m$-th Padovan and Perrin numbers respectively. Let $r, s$ be non-zero integers with $r\ge 1$ and $s\in \lbrace -1, 1\rbrace $, let $\lbrace U_n\rbrace _{n\ge 0}$ be the generalized Lucas sequence given by $U_{n+2}=rU_ ...
Odjoumani, Japhet +2 more
core +1 more source