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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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k-Generalized Pell Numbers Which are Concatenation of Two Repdigits
Mediterranean Journal of Mathematics, 2022Let \(\ge 2\) and let \((P_n^{(k)})_{n\ge -(k-2)}\) be the \(k\)-generalized Pell sequence defined by the recursion \(P_n^{(k)}=P_{n-1}^{(k)}+\cdots+P_{n-k}^{(k)}\) for \(n\ge 2\) with initial conditions \(0,0,\ldots,0,1\) (\(k-1\) zeros). They find all the members of this family of sequences which when written in base \(10\) are a concatenation of two
Zafer Şiar, Refik Keskin
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2023 International Conference on Computational Science and Computational Intelligence (CSCI), 2023
Weizheng Gao +6 more
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Weizheng Gao +6 more
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On the generalized k-Pell (p.i)-numbers.
Ars Comb., 2015The current article focus on the generalized k-Pell (p, i)-numbers for k = 1, 2, ... and 0
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Pell-Type Number Generators of Pythagorean Triples
1993It is well-known that primitive Pythagorean triples x, y, z can be generated by external generators M, N according to the equations $$ x = {M^2} - {N^2},\;\;y = 2MN,\,\,z = {M^2} + {N^2} $$ (1.1) where x, y, z, M, N are positive integers, (M, N) = 1 and M + N ≡ l(mod 2).
A. F. Horadam, A. G. Shannon
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