Results 1 to 10 of about 894 (158)
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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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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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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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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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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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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On Hybrid Numbers with Gaussian Leonardo Coefficients
Mathematics, 2023 We consider the Gaussian Leonardo numbers and investigate some of their amazing characteristic properties, including their generating function, the associated Binet formula and Cassini identity, and their matrix representation. Then, we define the hybrid
Nagihan Kara, Fatih Yilmaz
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Matrix Structure of Jacobsthal Numbers
Journal of Function Spaces, 2021 The main scenario of this paper is to introduce a new sequence of Jacobsthal type having a generalized order j. Some basic properties will be studied concerning it. Also, we will establish the generalized Binet formula.
Abdul Hamid Ganie, Mashael M. AlBaidani
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One-Parameter Generalization of Dual-Hyperbolic Jacobsthal Numbers
Annales Mathematicae Silesianae, 2023 In this paper, we introduce one-parameter generalization of dual-hyperbolic Jacobsthal numbers – dual-hyperbolic r-Jacobsthal numbers. We present some properties of them, among others the Binet formula, Catalan, Cassini, and d’Ocagne identities. Moreover,
Bród Dorota +2 more
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On Generalized Tribonacci Octonions
Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 2019 In this paper, we introduced generalized tribonacci octonion sequence which is a generalization of third order recurrence relations. We investigate many identities which are created by using generalized tribonacci sequence.
Arzu Özkoç Öztürk
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