Results 11 to 20 of about 1,194,375 (170)
Repdigits as sums of three Padovan numbers. [PDF]
Bol Soc Mat Mex, 2020 AbstractLet $$ \{P_{n}\}_{n\ge 0} $${Pn}n≥0 be the sequence of Padovan numbers defined by $$ P_0=0 $$P0=0, $$ P_1 =1=P_2$$P1=1=P2, and $$ P_{n+3}= P_{n+1} +P_n$$Pn+3=Pn+1+Pn for all $$ n\ge 0 $$n≥0. In this paper, we find all repdigits in base 10 which can be written as a sum of three Padovan numbers.
Ddamulira M.
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Matrix Sequences in terms of Padovan and Perrin Numbers [PDF]
Journal of Applied Mathematics, 2013 The first main idea of this paper is to develop the matrix sequences that represent Padovan and Perrin numbers. Then, by taking into account matrix properties of these new matrix sequences, some behaviours of Padovan and Perrin numbers will be ...
Nazmiye Yilmaz, Necati Taskara
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SymmetryIn this paper, we study a generalization of Padovan numbers. We define a generating function and matrix generators for the generalized Padovan sequence. Moreover, using graph methods and a special family of generalized Padovan sequences, we derive a multinomial formula for generalized Padovan numbers. We also prove some identities that generalize known
Małgorzata Wołowiec-Musiał +1 more
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Padovan numbers as sums over partitions into odd parts
Journal of Inequalities and Applications, 2016 Recently it was shown that the Fibonacci numbers can be expressed in terms of multinomial coefficients as sums over integer partitions into odd parts. In this paper, we introduce a similar representation for the Padovan numbers. As a corollary, we derive
Cristina Ballantine, Mircea Merca
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Some New Graph Interpretations of Padovan Numbers
SymmetryPadovan numbers and Perrin numbers belong to the family of numbers of the Fibonacci type and they are well described in the literature. In this paper, by studying independent (1,2)-dominating sets in paths and cycles, we obtain new binomial formulas for Padovan and Perrin numbers.
Iwona Włoch +2 more
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Padovan numbers that are concatenations of a Padovan number and a Perrin number
Periodica Mathematica HungaricaThe sequence of Padovan numbers defined by \(P_0 = P_1 = P_2 = 1; P_k = P_{k-2} + P_{k-3}\). The sequence of Perrin numbers defined by \(R_0 = 3, R_1 = 0, R_2 = 2; R_k = R_{k-2} + R_{k-3}\). The author determines all Padovan numbers which can be written as concatenations of a Padovan number and a Perrin number. Baker's method and Davenport reduction is
Merve Guney Duman
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Padovan numbers which are palindromic concatenations of two distinct repdigits [PDF]
Revista De La Real Academia De Ciencias Exactas, Fisicas Y Naturales - Serie A: Matematicas, 2021 International audienceIn this paper we determine all Padovan numbers that are palindromic concatenations of two ...
Mahadi Ddamulira, Taboka Chalebgwa
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On the bi-periodic Padovan sequences [PDF]
Mathematica Moravica, 2023 In this study, we define a new generalization of the Padovan numbers, which shall also be called the bi-periodic Padovan sequence. Also, we consider a generalized bi-periodic Padovan matrix sequence. Finally, we investigate the Binet formulas, generating
Dışkaya Orhan, Menken Hamza
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Padovan and Perrin Hybrid Number Identities
Communications in Advanced Mathematical Sciences, 2021 This work investigates the numbers of Padovan and Perrin hybrids. At first, the hybrid numbers, the sequences in the hybrid form, and their matrix forms are ordered as studied sequences. Thus, it was possible to display the negative index hybrids, define
Renata Vieira +3 more
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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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