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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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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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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 some identities belonging to these hybrid sequences, develop novel theorems and present them as ...
Renata VİEİRA +3 more
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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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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
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Padovan and Perrin numbers as products of two generalized Lucas numbers
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 +2 more
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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 thematrix sequencesthat 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 investigated.
Nazmiye Yilmaz, Necati Taskara
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Common terms of k-Pell numbers and Padovan or Perrin numbers
Arabian Journal of Mathematics, 2022 AbstractLet $$k\ge 2$$ k ≥ 2 . A generalization of the well-known Pell sequence is the k-Pell sequence. For this sequence, the first k terms are $$0,\ldots ,0,1$$ 0 ,
Benedict Vasco Normenyo +2 more
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Perrin numbers that are concatenations of two repdigits
Arabian Journal of Mathematics, 2022 AbstractLet $$ (P_n)_{n\ge 0}$$ ( P n ) n ≥ 0
Herbert Batte +2 more
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Perrin numbers and distinct repdigits [PDF]
, 2020 We determine all Perrin numbers that are concatenations of two repdigits.
Mahadi Ddamulira, Toboka Chalebgwa
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