Results 1 to 10 of about 25 (24)
Sums of generalized third-order Jacobsthal numbers by matrix methods
Trends in Computational and Applied MathematicsIn this paper, we consider a certain third-order linear recurrence and then give generating matrices for the sums of positively and negatively subscripted terms of this recurrence.
G. Cerda-Morales
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On Generalized Third-Order Jacobsthal Numbers
Asian Research Journal of Mathematics, 2021 In this paper, we investigate the generalized third order Jacobsthal sequences and we deal with, in detail, four special cases, namely, third order Jacobsthal, third order Jacobsthal-Lucas, modified third order Jacobsthal, third order Jacobsthal Perrin sequences.
Evren Eyican Polatlı, Yüksel Soykan
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On New Polynomial Sequences Constructed to Each Vertex in an n‐Gon
Discrete Dynamics in Nature and Society, Volume 2022, Issue 1, 2022., 2022 In this work, we bring to light the properties of newly formed polynomial sequences at each vertex of Pell polynomial sequences placed clockwise at each vertex in the n‐gon. We compute the relation among the polynomials with such vertices. Moreover, in an n‐gon, we generate a recurrence relation for a sequence giving the mth term formed at the kth ...
Abdul Hamid Ganie +4 more
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Introduction to Third-Order Jacobsthal and Modified Third-Order Jacobsthal Hybrinomials
Discussiones Mathematicae - General Algebra and Applications, 2021 The hybrid numbers are generalization of complex, hyperbolic and dual numbers. In this paper, we introduce and study the third-order Jacobsthal and modified third-order Jacobsthal hybrinomials, i.e., polynomials, which are a generalization of the ...
Cerda-Morales Gamaliel
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Non-Fisherian generalized Fibonacci numbers [PDF]
Notes on Number Theory and Discrete MathematicsUsing biology as inspiration, this paper explores a generalization of the Fibonacci sequence that involves gender biased sexual reproduction. The female, male, and total population numbers along with their associated recurrence relations are considered ...
Thor Martinsen
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A note on modified third-order Jacobsthal numbers
Proyecciones (Antofagasta), 2020 Modified third-order Jacobsthal sequence is defined in this study. Some properties involving this sequence, including the Binet-style formula and the generating function are also presented.
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The Third Order Jacobsthal Octonions: Some Combinatorial Properties
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2018 Various families of octonion number sequences (such as Fibonacci octonion, Pell octonion and Jacobsthal octonion) have been established by a number of authors in many di erent ways.
Cerda-Morales Gamaliel
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A Linear Functional Equation of Third Order Associated with the Fibonacci Numbers
Abstract and Applied Analysis, Volume 2014, Issue 1, 2014., 2014 Given a vector space X, we investigate the solutions f:R→X of the linear functional equation of third order f(x) = pf(x − 1) + qf(x − 2) + rf(x − 3), which is strongly associated with a well‐known identity for the Fibonacci numbers. Moreover, we prove the Hyers‐Ulam stability of that equation.
Soon-Mo Jung +2 more
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Complex Factorizations of the Lucas Sequences via Matrix Methods
Journal of Applied Mathematics, Volume 2014, Issue 1, 2014., 2014 Firstly, we show a connection between the first Lucas sequence and the determinants of some tridiagonal matrices. Secondly, we derive the complex factorizations of the first Lucas sequence by computing those determinants with the help of Chebyshev polynomials of the second kind. Furthermore, we also obtain the complex factorizations of the second Lucas
Honglin Wu, Mehmet Sezer
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Sequences of Non‐Gegenbauer‐Humbert Polynomials Meet the Generalized Gegenbauer‐Humbert Polynomials
International Scholarly Research Notices, Volume 2011, Issue 1, 2011., 2011 Here, we present a connection between a sequence of polynomials generated by a linear recurrence relation of order 2 and sequences of the generalized Gegenbauer‐Humbert polynomials. Many new and known transfer formulas between non‐Gegenbauer‐Humbert polynomials and generalized Gegenbauer‐Humbert polynomials are given.
Tian-Xiao He +4 more
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