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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
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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
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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
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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 +3 more
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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.
Seyyed Hossein Jafari Petroudi +1 more
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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
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Padovan numbers which are concatenations of three Padovan or Perrin numbers [PDF]
Notes on Number Theory and Discrete MathematicsThis 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
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A note on Mersenne Padovan and Perrin numbers [PDF]
Notes on Number Theory and Discrete Mathematics, 2021 In this paper, we determine all the Mersenne numbers which are in the sequences of Padovan and Perrin numbers, respectively.
Bir Kafle +2 more
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On the Richard and Raoul numbers
Journal of New Results in Science, 2022 In this study, we define and examine the Richard and Raoul sequences and we deal with, in detail, two special cases, namely, Richard and Raoul sequences. We indicate that there are close relations between Richard and Raoul numbers and Padovan and Perrin
Orhan Dışkaya, Hamza Menken
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Repdigits as products of consecutive Padovan or Perrin numbers [PDF]
Arabian Journal of Mathematics, 2021 AbstractA repdigit is a positive integer that has only one distinct digit in its decimal expansion, i.e., a number of the form $$a(10^m-1)/9$$ a ( 10 m - 1
Salah Eddine Rihane, Alain Togbé
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