Results 1 to 10 of about 11,331 (154)
A Note on Two Fundamental Recursive Sequences
Annales Mathematicae Silesianae, 2021 In this note, we establish some general results for two fundamental recursive sequences that are the basis of many well-known recursive sequences, as the Fibonacci sequence, Lucas sequence, Pell sequence, Pell-Lucas sequence, etc.
Farhadian Reza, Jakimczuk Rafael
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Some properties of bicomplex Pell and Pell-Lucas numbers
Journal of Information and Optimization Sciences, 2020 In this work, we investigated bicomplex Pell and Pell-Lucas numbers. We defined generating function and various identities involving both bicomplex Pell and Pell-Lucas numbers.
Karatas, Adnan, Halici, Serpil
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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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A Family of the Zeckendorf Theorem Related Identities [PDF]
, 2015 In this paper we present a family of identities for recursive sequences arising from a second order recurrence relation, that gives instances of Zeckendorf representation.
Martinjak, Ivica
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On the intersections of Fibonacci, Pell, and Lucas numbers [PDF]
, 2010 We describe how to compute the intersection of two Lucas sequences of the forms $\{U_n(P,\pm 1) \}_{n=0}^{\infty}$ or $\{V_n(P,\pm 1) \}_{n=0}^{\infty}$ with $P\in\mathbb{Z}$ that includes sequences of Fibonacci, Pell, Lucas, and Lucas-Pell numbers.
Bilu +13 more
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Smooth values of some quadratic polynomials [PDF]
, 2010 In this paper, using a method of Luca and the author, we find all values $x$ such that the quadratic polynomials $x^2+1,$ $x^2+4,$ $x^2+2$ and $x^2-2$ are 200-smooth and all values $x$ such that the quadratic polynomial $x^2-4$ is 100-smooth.Comment: 12 ...
Buchmann +6 more
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A New Generalization of Pell-Lucas Numbers (Bi-Periodic Pell-Lucas Sequence)
Communications in Mathematics and Applications, 2019 In this study, we bring into light, a new generalization of the Jacobsthal Lucas numbers, which shall also be called the bi-periodic Jacobsthal Lucas sequence as \begin{align*} Q_{n}= \begin{cases} 2bQ_{n-1}+Q_{n-2},&\text{if} \ n \ \text{is even} \\ 2aQ_{n-1}+Q_{n-2},&\text{if} \ n \ \text{is odd}% \end{cases} \text{\ \ }n\geq 2, \end{align*} with ...
Sukran Uygun, Hasan Karatas
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Sequences of Numbers Meet the Generalized Gegenbauer-Humbert Polynomials [PDF]
, 2011 Here we present a connection between a sequence of numbers generated by a linear recurrence relation of order 2 and sequences of the generalized Gegenbauer-Humbert polynomials.
Peter J.-S. Shiue +2 more
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Smarandache Sequence of Happy Cube Numbers [PDF]
, 2011 I have studied the Smarandache Happy Cube Numbers and I have got some interesting results and facts .
Muneer, Jebreel
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Abstract and Applied Analysis, 2014 Circulant matrices may play a crucial role in solving various differential equations. In this paper, the techniques used herein are based on the inverse factorization of polynomial.
Tingting Xu, Zhaolin Jiang, Ziwu Jiang
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