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Weighted Padovan graphs [PDF]

Discrete Mathematics
Weighted 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
exaly   +5 more sources

Combinatorial Interpretation of Numbers in the Generalized Padovan Sequence and Some of Its Extensions

Axioms, 2022
There is ongoing research into combinatorial methods and approaches for linear and recurrent sequences. Using the notion of a board defined for the Fibonacci sequence, this work introduces the Padovan sequence combinatorial approach.
Paula Catarino, Renata Passos Machado Vieira   +1 more
exaly   +2 more sources

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Counting on Padovan Numbers

The Fibonacci Quarterly
Arthur T Benjamin
exaly   +2 more sources

Combinatorial Identities for the Padovan Numbers

The Fibonacci Quarterly, 2019
We interpret the Padovan numbers combinatorially by having them count the number of tilings of an n-strip using dominoes and triominoes. Using this interpretation, we develop a collection of identities satisfied by the sequence of Padovan ...
Tedford, Steven J.
core   +3 more sources

On Concatenations of Two Padovan and Perrin Numbers

Bulletin of the Iranian Mathematical Society, 2023
Let \( (P_k)_{k\ge 0} \) and \( (R_k)_{k\ge 0} \) be the sequences of Padovan and Perrin numbers defined by the respective linear recurrence relations: \( P_0=0 \), \( P_1=P_2=1 \); \( P_k=P_{k-2}+P_{k-3} \) and \( R_0=3 \), \( R_1=0 \), \( R_2=2 \); \( R_k=R_{k-2}+R_{k-3} \), for \( k\ge 3 \).
openaire   +1 more source

Multiplicative Dependent Pairs in the Sequence of Padovan Numbers

Mathematica Slovaca, 2023
ABSTRACT The Padovan sequence {Pn } n≥0 is a ternary recurrent sequence defined recursively by the relation Pn = P n–2 + P n–3 with initials P 0 = P 1 = P
Behera, Mitashree, Ray, Prasanta Kumar
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Fibonacci numbers as sums of two Padovan numbers

Afrika Matematika, 2022
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ana Cecilia García Lomelí, Santos Hernández Hernández, Florian Luca   +2 more
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Hessenberg matrices and Padovan numbers

AIP Conference Proceedings, 2017
In this paper, we study the Padovan numbers and obtain some relationships between this sequence and permanent and determinant of a type of Hessenberg matrices.
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On b-concatenations of Padovan and Perrin numbers

Boletín de la Sociedad Matemática Mexicana
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kouèssi Norbert Adédji, Neelam Kandhil, Alain Togbé   +2 more
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Repdigits as sums of two Padovan numbers

J. Integer Seq., 2019
Let $ \{P_{n}\}_{n\geq 0} $ be the sequence of Padovan numbers given by $P_0=0, ~P_1= 1, ~P_2=1 \text{ and } P_{n+3}= P_{n+1}+P_n \text{ for all } n\geq 0$. This is the sequence $A000931$ on the Online Encyclopedia of Integer Sequences (OEIS). The first few terms of this sequence are \[\{P_{n}\}_{n\ge 0} = 0, 1, 1, 1, 2, 2, 3, 4, 5, 7, 9, 12, 16, 21 ...
Ana Cecilia García Lomelí, Santos Hernández Hernández   +1 more
openaire   +2 more sources