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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
core   +4 more sources

Generalized sum of Pell Numbers [PDF]

, 2021
Here we are proposing a generalized sum for Pell numbers. This sum contains four Pell numbers. By means of this generalized sum, the Pell number at position (n+m) in the sequence is given by the Pell numbers at positions n, m, (n-1) and (m-1).
Sparavigna, Amelia Carolina, Sparavigna, A. C.   +1 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
exaly   +2 more sources

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
exaly   +2 more sources

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
exaly   +5 more sources

An Exponential Diophantine Equation with Generalized Pell Numbers

Bulletin of the Brazilian Mathematical Society
Abstract For an integer $$k\ge 2$$ k ≥ 2
Jhon J Bravo, Florian Luca, Bravo Jhon J   +2 more
exaly   +2 more sources

Summing a Family of Generalized Pell Numbers [PDF]

Annales Mathematicae Silesianae, 2020
Abstract A new family of generalized Pell numbers was recently introduced and studied by Bród ([2]). These numbers possess, as Fibonacci numbers, a Binet formula. Using this, partial sums of arbitrary powers of generalized Pell numbers can be summed explicitly. For this, as a first step, a power
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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. That is, the generalized Pell number of order r ≥ 2; are expressed as a linear combination of a 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, with x, y, and z being k-generalized Pell numbers.
Julieth F. Ruiz, Jose L. Herrera, Jhon J. Bravo   +2 more
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Generalized Pell numbers, balancing numbers and binary quadratic forms [PDF]

Creative Mathematics and Informatics, 2014
In this work, we derive some algebraic identities on generalized Pell numbers and their relationship with balancing numbers. Also we deduce some results on binary quadratic forms involving Pell and balancing numbers.
TEKCAN, AHMET, MERVE, TAYAT
openaire   +2 more sources