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Discrete MathematicsWeighted Padovan graphs $Φ^{n}_{k}$, $n \geq 1$, $\lfloor \frac{n}{2} \rfloor \leq k \leq \lfloor \frac{2n-2}{3} \rfloor$, are introduced as the graphs whose vertices are all Padovan words of length $n$ with $k$ $1$s, two vertices being adjacent if one ...
Vesna Irsic, Sandi Klavžar, Elif Tan
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On Gaussian Jacobsthal-Padovan Numbers
Cumhuriyet Science Journal, 2022 Gaussian Jacobsthal-Padovan numbers have been the central focus of this paper and firstly this number sequence has defined. Later, we have given the proof of the generating function of the Gaussian Jacobsthal-Padovan sequence.
Nusret Karaaslan
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The Padovan numbers of the form 6a ± 6 b ± 6 c
Revista Integración, 2023 Let (Pn)n>0 be the Padovan sequence given by P0 = 0, P1 = P2 = 1 and the recurrence formula Pn+3 = Pn+1 + Pn for all n > 0. In this note, we completely solve the Diophantine equation Pn = 6a ± 6b ± 6c in non-negative integers (n, a, b, c) with a > b > c
Ana Cecilia García Lomelí +1 more
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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 Combinatorial Interpretation of the Padovan Generalized Polynomial Sequence
Armenian Journal of Mathematics, 2023 We investigate a combinatorial interpretation of the Padovan polynomial sequence, also addressing its polynomial extensions. We thus include the Tridovan polynomial sequence, Tetradovan polynomial sequences, leading up to the Z-dovan polynomial generalization.
Renata Passos Machado Vieira +2 more
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A STUDY ON BINOMIAL TRANSFORM OF THE GENERALIZED PADOVAN SEQUENCE
, 2022 In this paper, we define the binomial transform of the generalized Padovan sequence and as special cases, the binomial transform of the Padovan, Perrin, Padovan-Perrin, modified Padovan, adjusted Padovan sequences will be introduced. We investigate their
SOYKAN, YÜKSEL +5 more
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Common Values of Padovan and Perrin Sequences
Mediterranean Journal of Mathematics, 2023 AbstractThe integer sequence defined by$$P_{n+3}=P_{n+1}+P_{n}$$Pn+3=Pn+1+Pnwith initial conditions$$P_{0}=P_{1}=P_{2}=1$$P0=P1=P2=1is known as the Padovan sequence$$(P_{n})_{n\in \mathbb {Z}}$$(Pn)n∈Z. The Perrin sequence$$(R_{m})_{m\in \mathbb {Z}}$$(Rm)m∈Zsatisfies the same recurrence equation as the Padovan sequence but with starting values$$R_{0 ...
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On the Quinary Fibonacci-Padovan Sequences
Creative Mathematics and Informatics, 2022 In this paper, we consider the Fibonacci and Padovan sequences. We introduce the quinary Fibonacci-Padovan sequences whose compounds are the Fibonacci and Padovan sequences. We derive the Binet-like formulas, the generating functions and exponential generating functions of these sequences.
Dişkaya, Orhan, Menken, Hamza
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Relations on higher dimensional Padovan sequences [PDF]
Notes on Number Theory and Discrete Mathematics, 2021 Many papers developed so far for Padovan sequences properties and its extensions usually follow the one-dimensional approach. The presented work introduces new relations for a higher dimensional sequence, this approach is adopted for two, three and n-dimensional Padovan Sequence.
Renata Passos Machado Vieira +2 more
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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 thematrix sequencesthat 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 investigated.
Nazmiye Yilmaz, Necati Taskara
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