Results 1 to 10 of about 356 (132)
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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On a New One Parameter Generalization of Pell Numbers [PDF]
Annales Mathematicae Silesianae, 2019 In this paper we present a new one parameter generalization of the classical Pell numbers. We investigate the generalized Binet’s formula, the generating function and some identities for r-Pell numbers.
Bród Dorota
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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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Solutions of equations x2−(p2q2±3p)y2=±kt
Examples and Counterexamples, 2022 In the present paper, we have solved the equation x2−(p2q2±3p)y2=kt,x2−(p2q2±5p)y2=ktand expressed its positive integer solutions in terms of generalized Fibonacci, generalized Lucas and generalized Pell, generalized Pell–Lucas sequences.
Roji Bala, Vinod Mishra
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Mathematics, 2021 In this paper, we introduce and study a new two-parameters generalization of the Fibonacci numbers, which generalizes Fibonacci numbers, Pell numbers, and Narayana numbers, simultaneously.
Natalia Bednarz
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