Results 61 to 70 of about 1,051 (219)

On sums of k-generalized Fibonacci and k-generalized Lucas numbers as first and second kinds of Thabit numbers [PDF]

Notes on Number Theory and Discrete Mathematics
Let (Fᵣ⁽ᵏ⁾)ᵣ≥2-k and (Lᵣ⁽ᵏ⁾)ᵣ≥2-k be generalizations of the Fibonacci and Lucas sequences, where k≥2. For these sequences the initial k terms are 0,0,...,0, 1 and 0,0,...,2,1, and each subsequent term is the sum of the preceding k terms.
Hunar Sherzad Taher, Saroj Kumar Dash
doaj   +1 more source

Split Quaternionic Representations of Horadam Sequences and Their Binet, Generating Function, and Cassini‐Type Identities

Journal of Mathematics, Volume 2026, Issue 1, 2026.
This study establishes a novel algebraic connection between Horadam numbers and the split quaternion algebra. To this end, two fundamental constructs are introduced: the Fibonacci Sq,r‐split quaternions and the Horadam sq,r‐split quaternions, which generalize Horadam numbers within the framework of split quaternions.
İskender Öztürk, Hasan Çakır, Smritijit Sen   +2 more
wiley   +1 more source

On the Generalized Order-$k$ Fibonacci and Lucas Numbers

Rocky Mountain Journal of Mathematics, 2006
In this paper we consider the generalized order-k Fibonacci and Lucas numbers. We give the generalized Binet formula, combinatorial representation and some relations involving the generalized order-k Fibonacci and Lucas numbers.
Kiliç, Emrah, Taşci, Dursun
openaire   +4 more sources

High‐resolution X‐ray scanning with a diffuse Huffman‐patterned probe to reduce radiation damage

Journal of Synchrotron Radiation, Volume 32, Issue 3, Page 700-717, May 2025.
This paper introduces high‐resolution imaging using diffuse probes, which allow for lower energy deposition per unit area per unit time, by encoding Huffman‐like patterns onto them, enabling a tighter impulse response. The approach, demonstrated in X‐ray imaging, involves using specially fabricated masks to shape the probe and recover sharp object ...
Alaleh Aminzadeh, Andrew M. Kingston, Lindon Roberts, David M. Paganin, Timothy C. Petersen, Imants D. Svalbe   +5 more
wiley   +1 more source

Fibonacci and Lucas Numbers [PDF]

, 2017
U ovom diplomskom radu dan je uvod u Fibonaccijeve i Lucasove brojeve. U prvom dijelu rada definirali smo Fibonaccijeve i Lucasove brojeve, dokazali različite identitete koji vrijede za Fibonaccijeve brojeve, neke koji vrijede za Lucasove brojeve i ...
Zirdum, Ivona
core  

Novel Expressions for Certain Generalized Leonardo Polynomials and Their Associated Numbers

Axioms
This article introduces new polynomials that extend the standard Leonardo numbers, generalizing Fibonacci and Lucas polynomials. A new power form representation is developed for these polynomials, which is crucial for deriving further formulas.
Waleed Mohamed Abd-Elhameed, Omar Mazen Alqubori, Abdulrahim A. Alluhaybi, Amr Kamel Amin   +3 more
doaj   +1 more source

On some links between the generalised Lucas pseudoprimes of level k

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2023
Pseudoprimes are composite integers sharing behaviours of the prime numbers, often used in practical applications like public-key cryptography. Many pseudoprimality notions known in the literature are defined by recurrent sequences.
Andrica Dorin, Bagdasar Ovidiu, Rassias Michael Th.   +2 more
doaj   +1 more source

Narayana Numbers With Zeckendorf Partition in Two Terms

International Journal of Mathematics and Mathematical Sciences, Volume 2025, Issue 1, 2025.
The Narayan’s cow sequence starts with the terms 1, 1, and 1. Each subsequent term is obtained as the sum of the previous term and the term three places before. A term of this sequence is called a Narayana number. The mathematician Zeckendorf proved that every positive integer has a unique decomposition into a sum of distinct and nonconsecutive ...
Japhet Odjoumani, Salifou Nikiema, Shikha Binwal   +2 more
wiley   +1 more source

Convoluted convolved Fibonacci numbers

, 2020
The convolved Fibonacci numbers F (r) In this note we consider some related numbers that can be expressed in terms of convolved Fibonacci numbers. These numbers appear in the numerical evaluation of a constant arising in the study of the average density ...
Numbers Fibonacci, Pieter Moree, Convolved Convoluted, P Moree   +3 more
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Sums of certain products of fibonacci & Lucas numbers-part III [PDF]

, 2017
For the Fibonacci numbers, the summation formula σnk=1 Fk2=FnFn+1is well-known. Its charm lies in the fact that the right side is a product of terms from the Fibonacci sequence.
Melham, RS
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