Results 31 to 40 of about 90 (77)

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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Sphractal: Estimating the Fractal Dimension of Surfaces Computed from Precise Atomic Coordinates via Box‐Counting Algorithm

Advanced Theory and Simulations, Volume 7, Issue 6, June 2024.
The fractal dimension of a surface allows its degree of roughness to be characterized quantitatively. The 3D surface computed from precise atomic coordinates can be represented as either a voxelized point cloud or a mathematically exact surface. Sphractal is a Python package that estimates the fractal dimensions of such surfaces by computing their box ...
Jonathan Yik Chang Ting, Andrew Thomas Agars Wood, Amanda Susan Barnard   +2 more
wiley   +1 more source

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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Computing Some Topological Indices of Two Kinds of Dendrimer Graphs G[n] and H[n]

Journal of Mathematics, Volume 2024, Issue 1, 2024.
Dendrimer molecules are macromolecules which have many applications in nanosciences, drug delivery, biology, and different areas of sciences. Topological indices of chemical graph theory are numerical descriptor of a molecular structure. The dendrimer graph G[n] is obtained by attaching the new paths P9, joined each pendant vertex of G[n − 1] to ...
Hojat Kaviani, Lotfallah Pourfaraj, Huadong Su   +2 more
wiley   +1 more source

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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p-th order generalized Fibonacci cubes and maximal cubes in Fibonacci p-cubes

Discrete Mathematics
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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Image Encryption Using Quantum 3D Mobius Scrambling and 3D Hyper-Chaotic Henon Map. [PDF]

Entropy (Basel), 2023
Wang L, Ran Q, Ding J.
europepmc   +1 more source

Perfect codes in generalized Fibonacci cubes

, 2018
The {\em Fibonacci cube} of dimension $n$, denoted as $Γ\_n$, 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 $Γ\_n$ 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.
openaire   +3 more sources

The size of $k$-th order generalized Fibonacci cubes

Let $k\geq2$. Then the $k$-th order Fibonacci cube $Γ^{(k)}_{n}$ is the subgraph of the hypercube $Q_{n}$ induced by vertices without $k$ consecutive $1$s. The case $k=2$ corresponds to the classic Fibonacci cube $Γ_{n}$. There are three kinds of calculation formulas of the size of $Γ_{n}$: the iteration form $|E(Γ_{n})|=|E(Γ_{n-1})|+|E(Γ_{n-2})|+F_{n}$
Wei, Jianxin, Yang, Yujun
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