Results 1 to 10 of about 1,421 (176)
On a generalization of the Pell sequence [PDF]
Mathematica Bohemica, 2021 The Pell sequence $(P_n)_{n=0}^{\infty}$ is the second order linear recurrence defined by $P_n=2P_{n-1}+P_{n-2}$ with initial conditions $P_0=0$ and $P_1=1$.
Jhon J. Bravo +2 more
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Fibonacci-Like sequence associated with k-Pell, k-Pell-Lucas and Modified k-Pell sequences [PDF]
Journal of Applied Mathematics and Computational Mechanics, 2017 The main aim of the present article to introduce a generalization of Fibonacci sequence which is similar to k-Pell, k-Pell-Lucas, Modified k-Pell sequences and known as Fibonacci-Like sequence. After that we obtain some fundamental properties of Fibonacci-Like sequence such as Binet formulae of Fibonacci-Like sequence, binomial transform of the ...
Arfat Ahmad Wani +2 more
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On perfect powers in $k$-generalized Pell sequence [PDF]
Mathematica Bohemica, 2023 Let $k\geq2$ and let $(P_n^{(k)})_{n\geq2-k}$ be the $k$-generalized Pell sequence defined by \begin{equation*} P_n^{(k)}=2P_{n-1}^{(k)}+P_{n-2}^{(k)}+\cdots+P_{n-k}^{(k)} \end{equation*}for $n\geq2$ with initial conditions \begin{equation*} P_{-(k-2)}^{(
Zafer Şiar +2 more
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On the (s,t)-Pell and (s,t)-Pell–Lucas sequences and their matrix representations
Applied Mathematics Letters, 2012 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hasan Huseyin Gulec, Necati Taskara
exaly +5 more sources
Matrix Representation of Bi-Periodic Pell Sequence [PDF]
Journal of Mahani Mathematical Research, 2023 In this study, a generalization of the Pell sequence called bi-periodic Pell sequence is carried out to matrix theory. Therefore, we call this matrix sequence the bi-periodic Pell matrix sequence whose entries are bi-periodic Pell numbers.
Sukran UYGUN, Ersen Akıncı
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Repdigits in generalized Pell sequences [PDF]
Archivum Mathematicum, 2020 In this paper, the authors study the \(k\)-generalized Pell sequence, which starts with \(0,\ldots,0,1\) and satisfies the recurrence \(P_n^{(k)}=2P_{n-1}^{(k)}+P_{n-2}^{(k)}+\cdots+P_{n-k}^{(k)}\). They find all \(k\)-generalized Pell numbers which are repdigits, namely \(P_5^{(3)}=33\) and \(P_6^{(4)}=88\).
Bravo, Jhon J., Herrera, Jose L.
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Binomial Transform for Quadra Fibona-Pell Sequence and Quadra Fibona-Pell Quaternion
Universal Journal of Mathematics and Applications, 2022 The main object of the study is to consider the binomial transform for quadra Fibona-Pell sequence and quadra Fibona-Pell quaternion. In the paper, which consists of two parts in terms of the results found, the first step was taken for the sequence by ...
Eda Gündüz, Arzu Özkoç
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On the intersection of Padovan, Perrin sequences and Pell, Pell-Lucas sequences
Annales Mathematicae et Informaticae, 2021 Summary: In this paper, we find all the Padovan and Perrin numbers which are Pell or Pell-Lucas numbers.
Rihane, Salah Eddine, Togbé, Alain
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Powers in products of terms of Pell's and Pell–Lucas Sequences [PDF]
International Journal of Number Theory, 2015 In this paper, we consider the usual Pell and Pell–Lucas sequences. The Pell sequence [Formula: see text] is given by the recurrence un= 2un-1+ un-2with initial condition u0= 0, u1= 1 and its associated Pell–Lucas sequence [Formula: see text] is given by the recurrence vn= 2vn-1+ vn-2with initial condition v0= 2, v1= 2.
Bravo, Jhon J. +3 more
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A Note on Two Fundamental Recursive Sequences
Annales Mathematicae Silesianae, 2021 In this note, we establish some general results for two fundamental recursive sequences that are the basis of many well-known recursive sequences, as the Fibonacci sequence, Lucas sequence, Pell sequence, Pell-Lucas sequence, etc.
Farhadian Reza, Jakimczuk Rafael
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