Results 61 to 70 of about 183 (115)
A Hybrid Matrix-Based Cryptographic Framework Using Multiple Linear Recurrence Sequences
MathematicsIn this study, we propose a matrix-based transformation framework constructed from special integer sequences, including Fibonacci, Lucas, Pell, and Jacobsthal numbers.
Sukran Uygun
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Some infinite series summations involving linear recurrence relations of order 2 and 3 [PDF]
Notes on Number Theory and Discrete MathematicsThis paper extends known results of second and third order recursive sequences through extensive formulations of properties of the roots of their characteristic equations, some are old but most are new. They are applied to novel studies of Σₙ₌ₒ^∞ aₘₙ/10ⁿ⁺
Anthony G. Shannon +4 more
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ON THE SEQUENCES RELATED TO FIBONACCI AND LUCAS NUMBERS [PDF]
Journal of the Korean Mathematical Society, 2005 The sequences \(\{U_n\}_{n\geq 0}\) and \(\{V_n\}_{n\geq 0}\) are introduced by recurrence relations: \[ \begin{aligned} U_n &= (q- 2)(U_{n-2}- U_{n-4},\;n\geq 4,\\ V_n &= (q-2) V_{n-2}- V_{n-4},\;n\geq 4\end{aligned} \] with initial conditions \(U_0= 0\), \(U_1= 1\), \(U_2= 1\), \(U_4= q- 1\), \(V_0= 2\), \(V_1= 1\), \(V_2= q-1\), where \(q\geq 5\) is
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Applications of Lucas sequences in convergence and signal processing
Scientific ReportsIn this paper we propose a new perspective related to Lucas sequence with statistical and summability, some considerations have been given in connection with their applications of signal processing.
Majeed Ahmad Yousif +4 more
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Some New Generalizations Of The Lucas Sequence
, 2017 In this paper, we investigate the generalized Lucas, the generalized complex Lucas and the generalized dual Lucas sequence using the Lucas number. Also, we investigate special cases of these sequences. Furthermore, we give recurrence relations, vectors, the golden ratio and Binet’s formula for the generalized Lucas and the generalized dual Lucas ...
Torunbalcı Aydın, Fügen, Yüce, Salim
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Revista Mexicana de Ciencias Geológicas, 2018 We studied the Tiringueo section from the San Lucas Formation, located in the state of Michoacán, SW Mexico. The section is a flysch sequence consisting of a rhythmic deposit of shale, siltstone, and fine to medium graded sandstone interbedded with ...
Lourdes Omaña +2 more
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Exploring Generalized $2^k$-Fibonacci Sequence: A New Family of the Fibonacci Sequence
Communications in Advanced Mathematical SciencesThe focus of this paper is to study the $2^k$–Fibonacci sequence, which is defined for all integers $2^k$, and its connections with both the Fibonacci and the Fibonacci-Lucas sequences.
Elis Gardel Costa Mesquista +2 more
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Tridiagonal matrices representations of generalized bivariate complex polynomials
Journal of Innovative Applied Mathematics and Computational SciencesThis paper introduces a closed-form expression for generalized bivariate complex polynomials using a tridiagonal determinant in symbolic form. Subsequences with even and odd indices are also represented as tridiagonal determinants.
K. L. Verma
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The American Journal of CombinatoricsUsing Postnikov's Le-diagrams, decorated permutations, and Grassmann necklaces, we classify which positroids are sparse paving matroids. This allows us to enumerate sparse paving positroids, making connections to a known sequence involving the golden ...
John Machacek, George Nasr
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, 2013 In this short paper, we prove, by only using elementary tools, general cases when $U_n(P,Q) \neq \square$, where $U_n(P,Q)$ is the Lucas sequence of the first type.
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