Results 1 to 10 of about 623 (119)
On Generalized Pell Numbers of Order r ≥ 2
Trends in Computational and Applied Mathematics, 2021 In this paper we investigate the generalized Pell numbers of order r ≥ 2 through the properties of their related fundamental system of generalized Pell numbers.
E. V. Pereira Spreafico, M. Rachidi
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Markov Triples with Generalized Pell Numbers
Mathematics, 2023 For an integer k≥2, let (Pn(k))n be the k-generalized Pell sequence which starts with 0,…,0,1 (k terms), and each term afterwards is given by Pn(k)=2Pn−1(k)+Pn−2(k)+⋯+Pn−k(k). In this paper, we determine all solutions of the Markov equation x2+y2+z2=3xyz,
Julieth F. Ruiz +2 more
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On Generalized Pell and Pell–Lucas Numbers [PDF]
Iranian Journal of Science and Technology, Transaction A: Science, 2019 In this paper, we introduce and study a new one-parameter generalization of Pell numbers. We describe their distinct properties also related to matrix representation.
Lucyna Trojnar-Spelina, Iwona Włoch
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On the sum of the reciprocals of $$\pmb {k}$$-generalized Pell numbers
Indian Journal of Pure and Applied Mathematics, 2023 Let \( \{P_{n}^{(k)}\}_{n\ge -(k-2)} \) be the \( k \)-generalized Pell sequence given by \begin{align*} P_n^{(k)}=2P_{n-1}^{(k)}+\cdots +P_{n-k}^{(k)}\quad \text{for all }\quad n\ge 2, \end{align*} with the initial conditions \begin{align*} P_{-(n-2)}^{(k)}=P_{-(n-3)}^{(k)}=\cdots =P_{0}^{(k)}=0 \quad \text{and} \quad P_{1}^{(k)}=1. \end{align*} When \
Benedict Vasco Normenyo
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THE GENERALIZED BINET FORMULA, REPRESENTATION AND SUMS OF THE GENERALIZED ORDER-$k$ PELL NUMBERS
Taiwanese Journal of Mathematics, 2006 In this paper we give a new generalization of the Pell numbers in matrix representation. Also we extend the matrix representation and we show that the sums of the generalized order-k Pell numbers could be derived directly using this representation. Further we present some identities, the generalized Binet formula and combinatorial representation of the
Emrah Kilic
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An Exponential Diophantine Equation with Generalized Pell Numbers
Bulletin of the Brazilian Mathematical SocietyAbstract For an integer $$k\ge 2$$ k ≥ 2
Jhon Jairo Bravo Grijalba +2 more
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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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Fermat and Mersenne numbers in $k$-Pell sequence
Математичні Студії, 2021 For an integer $k\geq 2$, let $(P_n^{(k)})_{n\geq 2-k}$ be the $k$-generalized Pell sequence, which starts with $0,\ldots,0,1$ ($k$ terms) and each term afterwards is defined by the recurrence $ P_n^{(k)}=2P_{n-1}^{(k)}+P_{n-2}^{(k)}+\cdots +P_{n-k}^{(k)}
B. Normenyo, S. Rihane, A. Togbe
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Properties of hyperbolic generalized Pell numbers [PDF]
Notes on Number Theory and Discrete Mathematics, 2020 In this paper, we introduce the generalized hyperbolic Pell numbers over the bidimensional Clifford algebra of hyperbolic numbers. As special cases, we deal with hyperbolic Pell and hyperbolic Pell–Lucas numbers. We present Binet’s formulas, generating functions and the summation formulas for these numbers.
Melih Göcen, Yüksel Soykan
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On some new results for the generalised Lucas sequences
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2021 In this paper we introduce the functions which count the number of generalized Lucas and Pell-Lucas sequence terms not exceeding a given value x and, under certain conditions, we derive exact formulae (Theorems 3 and 4) and establish asymptotic limits ...
Andrica Dorin +2 more
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