Results 11 to 20 of about 461 (158)

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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Algorithm for Constructing an Analogue of the Binet Formula [PDF]

Programming and Computer Software, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kuzovatov, V. I., Kytmanov, A. A., Kuzovatova, O. I.   +2 more
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Hybrid Quaternions of Leonardo

Trends in Computational and Applied Mathematics, 2022
In this article, we intend to investigate the Leonardo sequence presenting the hybrid Leonardo quaternions. To explore Hybrid Quaternions of Leonardo, the priori, sequence of Leonardo, quaternions and hybrid numbers were presented.
M. C. S. Mangueira, F. R. V. Alves, P. M. M. C. Catarino   +2 more
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On Quaternion Gaussian Bronze Fibonacci Numbers

Annales Mathematicae Silesianae, 2022
In the present work, a new sequence of quaternions related to the Gaussian Bronze numbers is defined and studied. Binet’s formula, generating function and certain properties and identities are provided.
Catarino Paula, Ricardo Sandra
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Extending generalized Fibonacci sequences and their binet-type formula [PDF]

Advances in Difference Equations, 2006
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Saeki Osamu, Rachidi Mustapha
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Dual Jacobsthal Quaternions

Communications in Advanced Mathematical Sciences, 2020
In this paper, dual Jacobsthal quaternions were defined. Also, the relations between dual Jacobsthal quaternions which connected with Jacobsthal and Jacobsthal-Lucas numbers were investigated. Furthermore, Binet's formula, Honsberger identity, D'ocagne'
Fügen Torunbalcı Aydın
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Higher-Order Jacobsthal–Lucas Quaternions

Axioms, 2022
In this work, we define higher-order Jacobsthal–Lucas quaternions with the help of higher-order Jacobsthal–Lucas numbers. We examine some identities of higher-order Jacobsthal–Lucas quaternions. We introduce their basic definitions and properties.
Mine Uysal, Engin Özkan
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Some identities of bivariate Pell and bivariate Pell-Lucas polynomials

Journal of Amasya University the Institute of Sciences and Technology, 2023
In this paper, we obtain some identities for the bivariate Pell polynomials and bivariate Pell-Lucas polynomials. We establish some sums and connection formulas involving them.
Yashwant Panwar
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The Fibonacci Numbers -- Exposed More Discretely [PDF]

, 2003
No abstract provided in this ...
Benjamin, Arthur T., Quinn, Jennifer J.
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Hyperbolic Fibonacci Sequence

Universal Journal of Mathematics and Applications, 2019
In this paper, we investigate the hyperbolic Fibonacci sequence and the hyperbolic Fibonacci numbers. Furthermore, we give recurrence relations, the golden ratio and Binet's formula for the hyperbolic Fibonacci sequence and Lorentzian inner product ...
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