Results 1 to 10 of about 878 (140)
Extending generalized Fibonacci sequences and their binet-type formula [PDF]
Advances in Difference Equations, 2006 We study the extension problem of a given sequence defined by a finite order recurrence to a sequence defined by an infinite order recurrence with periodic coefficient sequence.
Saeki Osamu, Rachidi Mustapha
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Generalization of the 2-Fibonacci sequences and their Binet formula [PDF]
Notes on Number Theory and Discrete MathematicsWe will explore the generalization of the four different 2-Fibonacci sequences defined by Atanassov. In particular, we will define recurrence relations to generate each part of a 2-Fibonacci sequence, discuss the generating function and Binet formula of ...
Timmy Ma, Richard Vernon, Gurdial Arora
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A combined approach to Perrin and Padovan hybrid sequences [PDF]
Heliyon, 2021 Recently, there has been huge interest to a new numeric set, which brings together three numerical systems: complex, hyperbolic and dual numbers, called as hybrid number.
Seyyed H. Jafari Petroudi +3 more
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The Representation, Generalized Binet Formula and Sums of The Generalized Jacobsthal p-Sequence
Hittite Journal of Science and Engineering, 2016 In this study, a new generalization of the usual Jacobsthal sequence is presented, which is called the generalized Jacobsthal Binet formula, the generating functions and the combinatorial representations of the generalized Jacobsthal p-sequence are ...
Ahmet Daşdemir
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Multiparameter Quantum Cauchy-Binet Formulas [PDF]
Algebras and Representation Theory, 2020 The quantum Cayley-Hamilton theorem for the generator of the reflection equation algebra has been proven by Pyatov and Saponov, with explicit formulas for the coefficients in the Cayley-Hamilton formula. However, these formulas do not give an \emph{easy} way to compute these coefficients.
Karlin, Samuel, Rinott, Yosef
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On the bivariate Padovan polynomials matrix [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 In this paper, we intruduce the bivariate Padovan sequence we examine its various identities. We define the bivariate Padovan polynomials matrix. Then, we find the Binet formula, generating function and exponential generating function of the bivariate ...
Orhan Dişkaya +2 more
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Matrix Representation of Bi-Periodic Pell Sequence [PDF]
Journal of Mahani Mathematical Research, 2023 In this study, a generalization of the Pell sequence called bi-periodic Pell sequence is carried out to matrix theory. Therefore, we call this matrix sequence the bi-periodic Pell matrix sequence whose entries are bi-periodic Pell numbers.
Sukran UYGUN, Ersen Akıncı
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Some properties and extended Binet’s formula for the class of bifurcating Fibonacci sequence
Ratio MathematicaOne of the generalizations of Fibonacci sequence is a -Fibonacci sequence, which is further generalized in several other ways, some by conserving the initial conditions and others by conserving the related recurrence relation.
Daksha Manojbhai Diwan +2 more
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Some geometric properties of the Padovan vectors in Euclidean 3-space [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 Padovan numbers were defined by Stewart (1996) in honor of the modern architect Richard Padovan (1935) and were first discovered in 1924 by Gerard Cordonnier.
Serdar Korkmaz, Hatice Kuşak Samancı
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The generalized Binet formula for $k$-bonacci numbers
Elemente der Mathematik, 2023 Using Vandermonde determinants, we give a simple proof of the generalization of the Binet formula to the k -bonacci numbers.
Parks, Harold R., Wills, Dean C.
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