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Fibonacci numbers in generalized Pell sequences
Mathematica Slovaca, 2020Abstract In this paper, by using lower bounds for linear forms in logarithms of algebraic numbers and the theory of continued fractions, we find all Fibonacci numbers that appear in generalized Pell sequences. Some interesting estimations involving generalized Pell numbers, that we believe are of independent interest, are also deduced ...
Jhon Jairo Bravo Grijalba +1 more
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Even perfect numbers in generalized Pell sequences
Lithuanian Mathematical Journal, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jhon Jairo Bravo Grijalba +1 more
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On the computing of the generalized order-k Pell numbers in log time
Applied Mathematics and Computation, 2006 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Emrah Kiliç +2 more
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On the generalized k-Pell (p.i)-numbers.
Ars Comb., 2015 The current article focus on the generalized k-Pell (p, i)-numbers for k = 1, 2, ... and 0
Arı, Kamil
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Mathematics Seminar Notes, 1978
Define the sequence \(\{R_n\}\) by integers \(R_0\), \(R_1\), and the recurrence relation \(R_n=2R_{n-1}+R_{n-2}\) \((n>1)\). If the equation \(x^2-2y^2=N\) has integer solutions, then all the solutions are given by finitely many sequences \(\{R_n\}\) and \((x;y)=\left(\pm (R_{2n}+R_{2n+1}); \pm R_{2n+1}\right)\).
Kiss, Péter, Várnai, Ferenc
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Define the sequence \(\{R_n\}\) by integers \(R_0\), \(R_1\), and the recurrence relation \(R_n=2R_{n-1}+R_{n-2}\) \((n>1)\). If the equation \(x^2-2y^2=N\) has integer solutions, then all the solutions are given by finitely many sequences \(\{R_n\}\) and \((x;y)=\left(\pm (R_{2n}+R_{2n+1}); \pm R_{2n+1}\right)\).
Kiss, Péter, Várnai, Ferenc
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A generalization of generalized Fibonacci and generalized Pell numbers
International Journal of Mathematical Education in Science and Technology, 2016This paper is concerned with developing a new class of generalized numbers. The main advantage of this class is that it generalizes the two classes of generalized Fibonacci numbers and generalized Pell numbers. Some new identities involving these generalized numbers are obtained.
W.M. Abd-Elhameed, N.A. Zeyada
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Combinatorial interpretation of generalized Pell numbers
J. Integer Seq., 2020Summary: In this note we give combinatorial interpretations for the generalized Pell sequence of order \(k\) by means of lattice paths and generalized bi-colored compositions. We also derive some basic relations and identities by using Riordan arrays.
Jhon J. Bravo +2 more
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Generalized Identities for third order Pell Number, Pell-Lucas Number and Modified Pell Number
2020วารสารวิทยาศาสตร์และเทคโนโลยี มทร.ธัญบุรี, 10, 1, 96 ...
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Generalized Pell Numbers and Polynomials
2004We define sequences of generalized Pell numbers with the notation introduced by Horadam [6] $$ \left\{ {{P_{r,n}}} \right\} \equiv \left\{ {{P_{r,n}}\left( {1,\,{2^r};\,{2^r}, - 1} \right)} \right\} $$ (1.1) and by the second order recurrence relation $$ {P_{r,n}} = {2^r}{P_{r,n - 1}} + {P_{r,n - 2}},\quad n > 2 $$ (1.2) with ...
A. G. Shannon, A. F. Horadam
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Integral Aspects of the Generalized Pell and Pell-Lucas Numbers
International Journal of Mathematics and Computer ScienceIn this paper, we propose integral representations of the one-parameter k-Pell and k-Pell-Lucas numbers. Our results are also deduced with the Pell and Pell-Lucas numbers.
Achariya Nilsrakoo, Weerayuth Nilsrakoo
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