Results 31 to 40 of about 648 (170)
On some properties of k-circulant matrices with the generalized Pell-Padovan numbers
Journal of Innovative Applied Mathematics and Computational SciencesIn this paper, we investigate the properties of the $k$-circulant matrix generated by the generalized Pell--Padovan numbers. We derive explicit formulas for the sum of entries, the maximum column sum norm ($\Vert \cdot \Vert _{1}$), the maximum row sum ...
Yüksel Soykan, Erkan Taşdemir
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Determinants of the RFMLR Circulant Matrices with Perrin, Padovan, Tribonacci, and the Generalized Lucas Numbers [PDF]
Journal of Applied Mathematics, 2014 The row first-minus-last right (RFMLR) circulant matrix and row last-minus-first left (RLMFL) circulant matrices are two special pattern matrices. By using the inverse factorization of polynomial, we give the exact formulae of determinants of the two ...
Zhaolin Jiang, Nuo Shen, Juan Li
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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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Padovan Numbers as Sum of Two Repdigits
Proceedings of the Bulgarian Academy of Sciences, 2023 Padovan sequence $$(P_{n})$$ is given by $$P_{n}=P_{n-2}+P_{n-3}$$ for $$n\geq3$$ with initial condition $$(P_{0},P_{1},P_{2})=(1,1,1)$$. A positive integer is called a repdigit if all of its digits are equal. In this study, we examine the terms of the Padovan sequence, which are the sum of two repdigits.
Duman, Merve Güney +5 more
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De Moivre-Type Identities for the Padovan Numbers [PDF]
, 2021 At this work, we give a method for constructing the Perrin and Padovan sequences and obtain the De Moivre-type identity for Padovan numbers. Also, we define a Padovan sequence with new initial conditions and find some identities between all of these ...
Akbıyık, Mücahit +2 more
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New Types of Distance Padovan Sequences via Decomposition Technique
Applied Sciences, 2022 In this paper, we introduce new kinds of generalized Padovan sequences and study their properties using number decomposition techniques. In particular, we consider three types of generalized Padovan sequences defined by the same recurrence equation with ...
Andrzej Włoch +2 more
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Compositions of positive integers with 2s and 3s
Demonstratio Mathematica, 2023 In this article, we consider compositions of positive integers with 2s and 3s. We see that these compositions lead us to results that involve Padovan numbers, and we give some tiling models of these compositions.
Dişkaya Orhan, Menken Hamza
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On the Richard and Raoul numbers
Journal of New Results in Science, 2022 In this study, we define and examine the Richard and Raoul sequences and we deal with, in detail, two special cases, namely, Richard and Raoul sequences. We indicate that there are close relations between Richard and Raoul numbers and Padovan and Perrin
Orhan Dışkaya, Hamza Menken
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A note on Pell-Padovan numbers and their connection with Fibonacci numbers
Karpatsʹkì Matematičnì Publìkacìï, 2020 In this paper, we find new relations involving the Pell-Padovan sequence which arise as determinants of certain families of Toeplitz-Hessenberg matrices. These determinant formulas may be rewritten as identities involving sums of products of Pell-Padovan
T.P. Goy, S.V. Sharyn
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Summing Formulas for Generalized Tribonacci Numbers
Universal Journal of Mathematics and Applications, 2020 In this paper, closed forms of the summation formulas for generalized Tribonacci numbers are presented. Then, some previous results are recovered as particular cases of the present results.
Yüksel Soykan
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