Results 11 to 20 of about 64 (61)

A negative answer to a problem on generalized Fibonacci cubes

Discrete Mathematics, 2017
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jianxin Wei, Heping Zhang
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Generalized Fibonacci and Lucas cubes arising from powers of paths and cycles

Discrete Mathematics, 2016
19 pages.
P. Codara, O.M. D’Antona
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The existence of perfect codes in a family of generalized Fibonacci cubes [PDF]

Information Processing Letters, 2018
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On Sums of Cubes of Generalized Fibonacci Numbers: Closed Formulas of Σn k=0 kW3 k and Σn k=1 kW3− k

Asian Research Journal of Mathematics, 2020
In this paper, closed forms of the sum formulas Σn k=0 kW3 k and Σn k=1 kW3-k for the cubes of generalized Fibonacci numbers are presented. As special cases, we give sum formulas of Fibonacci, Lucas, Pell, Pell-Lucas, Jacobsthal, Jacobsthal-Lucas numbers. We present the proofs to indicate how these formulas, in general, were discovered.
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Closed Formulas for the Sums of Cubes of Generalized Fibonacci Numbers: Closed Formulas of Σn k=0W3 Σ k and n k=1W3

Archives of Current Research International, 2020
In this paper, closed forms of the sum formulas for the cubes of generalized Fibonacci numbers are presented. As special cases, we give summation formulas of Fibonacci, Lucas, Pell, Pell-Lucas, Jacobsthal and Jacobsthal-Lucas numbers.
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A Study on Generalized Fibonacci Numbers: Sum Formulas $\sum_{k=0}^{n}kx^{k}W_{k}^{3}$ and $\sum_{k=1}^{n}kx^{k}W_{-k}^{3}$ for the Cubes of Terms

Earthline Journal of Mathematical Sciences, 2020
In this paper, closed forms of the sum formulas $\sum_{k=0}^{n}kx^{k}W_{k}^{3}$ and $\sum_{k=1}^{n}kx^{k}W_{-k}^{3}$ for the cubes of generalized Fibonacci numbers are presented. As special cases, we give sum formulas of Fibonacci, Lucas, Pell, Pell-Lucas, Jacobsthal, Jacobsthal-Lucas numbers.
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Perfect codes in generalized Fibonacci cubes

, 2018
The {\em Fibonacci cube} of dimension $n$, denoted as $ \_n$, is the subgraph of the $n$-cube $Q\_n$ induced by vertices with no consecutive 1's. In an article of 2016 Ashrafi and his co-authors proved the non-existence of perfect codes in $ \_n$ for $n\geq 4$.
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A Study On Sums of Cubes of Generalized Fibonacci Numbers: Closed Formulas of $\sum_{k=0}^{n}x^{k}W_{k}^{3}$ and $\sum_{k=1}^{n}x^{k}W_{-k}^{3} $

, 2020
In this paper, closed forms of the sum formulas $\sum_{k=0}^{n}x^{k}W_{k}^{3}$ and $\sum_{k=1}^{n}x^{k}W_{-k}^{3}$ for the cubes of generalized Fibonacci numbers are presented. As special cases, we give sum formulas of Fibonacci, Lucas, Pell, Pell-Lucas, Jacobsthal, Jacobsthal-Lucas numbers.
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Image Encryption Using Quantum 3D Mobius Scrambling and 3D Hyper-Chaotic Henon Map. [PDF]

Entropy (Basel), 2023
Wang L, Ran Q, Ding J.
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$p$-th order generalized Fibonacci cubes and maximal cubes in Fibonacci $p$-cubes

The Fibonacci cube $Γ_n$ is the subgraph of the hypercube $Q_n$ induced by vertices with no consecutive 1s. We study a one parameter generalization, p-th order Fibonacci cubes $Γ^{(p)}_n$, which are subgraphs of $Q_n$ induced by strings without p consecutive 1s. We show the link between vertices of $Γ^{(p)}_n$ and compositions of integers with parts in
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