Results 11 to 20 of about 1,266,662 (229)

Matrix Sequences in terms of Padovan and Perrin Numbers [PDF]

Journal of Applied Mathematics, 2013
The first main idea of this paper is to develop the matrix sequences that represent Padovan and Perrin numbers. Then, by taking into account matrix properties of these new matrix sequences, some behaviours of Padovan and Perrin numbers will be ...
Nazmiye Yilmaz, Necati Taskara
doaj   +8 more sources

Padovan and Perrin Hybrid Number Identities

Communications in Advanced Mathematical Sciences, 2021
This work investigates the numbers of Padovan and Perrin hybrids. At first, the hybrid numbers, the sequences in the hybrid form, and their matrix forms are ordered as studied sequences. Thus, it was possible to display the negative index hybrids, define
Renata Vieira, Milena Mangueira, Francisco Regis Alves, Paula Maria Machado Cruz Catarino   +3 more
doaj   +3 more sources

A combined approach to Perrin and Padovan hybrid sequences

Heliyon, 2021
Recently, there has been huge interest to a new numeric set, which brings together three numerical systems: complex, hyperbolic and dual numbers, called as hybrid number.
Fatih Yilmaz, Emel Karaca, Seyyed Hossein Jafari Petroudi   +2 more
exaly   +3 more sources

Hessenberg matrices and the Pell and Perrin numbers

Journal of Number Theory, 2011
AbstractIn this paper, we investigate the Pell sequence and the Perrin sequence and we derive some relationships between these sequences and permanents and determinants of one type of Hessenberg matrices.
Fatih Yilmaz, Durmus Bozkurt
exaly   +4 more sources

k-Fibonacci numbers which are Padovan or Perrin numbers

Indian Journal of Pure and Applied Mathematics, 2022
Let \( \{P_m\}_{m\ge 0} \) be the sequence of Padovan numbers defined by the linear recurrence: \( P_0=P_1=P_2=1 \), and \( P_{m+3}=P_{m+1}+P_m \) for all \( m\ge 0 \). Also, let \( \{E_m\}_{m\ge 0} \) be the sequence of Perrin numbers defined by the linear recurrence: \( E_0=3,~E_1=0,~E_2=2 \), and \( E_{m+3}=E_{m+1}+E_m \) for all \( m\ge 0 ...
Salah Eddine Rihane, Alain Togbé
exaly   +2 more sources

Padovan and Perrin numbers as products of two generalized Lucas numbers [PDF]

Archivum Mathematicum, 2023
Let \(P_m\) and \(E_m\) be the \(m\)th Padovan and Perrin numbers, respectively. Let \(r,s\in \mathbb{Z}\) with \(r\ge 1\) and \(s\in\{-1,1\}\), and let \(\{U_n\}_{n\ge 0}\) be the generalized Lucas sequence given by \[U_0=0,\quad U_1=1\quad\mbox{and}\quad U_{n+2}=rU_{n+1}+sU_n.\] In the paper under review, the authors give effective bounds for the ...
Adédji, Kouèssi Norbert, Odjoumani, Japhet, Togbé, Alain   +2 more
openaire   +3 more sources

Bipartite Graphs Associated with Pell, Mersenne and Perrin Numbers [PDF]

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2019
In this paper, we consider the relationships between the numbers of perfect matchings (1-factors) of bipartite graphs and Pell, Mersenne and Perrin Numbers.
Öteleş Ahmet
doaj   +2 more sources

Padovan numbers which are concatenations of three Padovan or Perrin numbers [PDF]

Notes on Number Theory and Discrete Mathematics
This paper presents all Padovan numbers that can be written as the concatenation of three Padovan or Perrin numbers under a certain constraint. Namely, we consider the Diophantine equations Pₜ=10ᵈ⁺ˡPₘ+10ˡPₙ+Pᵣ and Pₜ=10ᵈ⁺ˡRₘ+10ˡRₙ+Rᵣ, where k,m,n,r,d and
Fatih Erduvan
doaj   +2 more sources

Determinants of the RFMLR Circulant Matrices with Perrin, Padovan, Tribonacci, and the Generalized Lucas Numbers [PDF]

Journal of Applied Mathematics, 2014
The row first-minus-last right (RFMLR) circulant matrix and row last-minus-first left (RLMFL) circulant matrices are two special pattern matrices. By using the inverse factorization of polynomial, we give the exact formulae of determinants of the two ...
Zhaolin Jiang, Nuo Shen, Juan Li
doaj   +4 more sources

Perrin Numbers That Are Concatenations of a Perrin Number and a Padovan Number in Base b

Symmetry
Let (Pk)k≥0 be a Padovan sequence and (Rk)k≥0 be a Perrin sequence. Let n, m, b, and k be non-negative integers, where 2≤b≤10. In this paper, we are devoted to delving into the equations Rn=bdPm+Rk and Rn=bdRm+Pk, where d is the number of digits of Rk or Pk in base b. We show that the sets of solutions are Rn∈{R5,R6,R7,R8,R9,R10,R11,R12,R13,R14,R15,R16,
Merve Guney Duman
exaly   +3 more sources