Results 101 to 110 of about 616 (205)

Determinant Representations of Sequences: A Survey

Special Matrices, 2014
This is a survey of recent results concerning (integer) matrices whose leading principal minors are well-known sequences such as Fibonacci, Lucas, Jacobsthal and Pell (sub)sequences. There are different ways for constructing such matrices.
Moghaddamfar A. R., Salehy S. Navid, Salehy S. Nima   +2 more
doaj   +1 more source

An algorithm for complex factorization of the bi-periodic Fibonacci and Lucas polynomials [PDF]

Notes on Number Theory and Discrete Mathematics
In this paper, we consider the factorization of generalized sequences, by employing a method based on trigonometric identities. The new method is of reduced complexity and represents an improvement compared to existing results.
Baijuan Shi, Can Kızılateş
doaj   +1 more source

Some basic properties of the generalized bi-periodic Fibonacci and Lucas sequences

Advances in Difference Equations, 2020
In this paper, we consider a generalization of Horadam sequence {wn} $\{ w_{n} \} $ which is defined by the recurrence relation wn=χ(n)wn−1+cwn−2 $w_{n}=\chi ( n ) w_{n-1}+cw_{n-2}$, where χ(n)=a $\chi ( n ) =a$ if n is even, χ(n)=b $\chi ( n ) =b$ if n ...
Elif Tan, Ho-Hon Leung
doaj   +1 more source

Generalized bi-periodic Fibonacci sequences and their matrix representations [PDF]

, 2022
Bu tez beş bölümden oluşmaktadır. Birinci bölüm giriş kısmına ayrılmıştır. İkinci bölümde, Fibonacci ve Lucas dizilerinin genelleştirilmesinden ve Horadam dizisinin temel özelliklerinden bahsedilmiştir.
Özden, Tuğba
core  

Genelleştirilmiş Fibonacci ve Lucas dizileri ve bazı uygulamaları [PDF]

, 2010
06.03.2018 tarihli ve 30352 sayılı Resmi Gazetede yayımlanan “Yükseköğretim Kanunu İle Bazı Kanun Ve Kanun Hükmünde Kararnamelerde Değişiklik Yapılması Hakkında Kanun” ile 18.06.2018 tarihli “Lisansüstü Tezlerin Elektronik Ortamda Toplanması ...
Demirtürk, Bahar
core  

Visualization of Metallic Sequences and its Extensions: A Combinatorial approach Via Board and Tiles

REDIMAT
The study of recurring numerical sequences interests numerous researchers in several countries. We observe that, with a historical legacy from the Fibonacci and Lucas sequences, numerous ways of approaching and generalizing these and other sequences ...
Francisco Regis Vieira Alves, Maria Graciene Moreira Dos Santos, Paula Maria Machado Cruz Catarino   +2 more
doaj   +1 more source

Diophantine triples with values in the sequences of Fibonacci and Lucas numbers

Glasnik matematički, 2017
Let FL={1,2,3,4,5,7,8,11,13,18,21, … } be the set consisting of all Fibonacci and Lucas numbers with positive subscripts. We find all triples (a,b,c) of positive integers a < b < c such that ab+1, ac+1, bc+1 are all members of FL.
Luca, Florian, Munagi, Augustine O.
openaire   +3 more sources

On the periods of bi-periodic Fibonacci and bi-periodic Lucas sequences [PDF]

, 2017
Bu tez çalışmasında k-Lucas dizisi için Pisano periyodu ve bu periyot ile ilgili özellikler verilmiştir. Ayrıca k-Fibonacci ile k-Lucas dizilerinin 2^n moduna göre periyotları incelenmiştir.
Kızılırmak, Gül Özkan
core  

The bi-periodic Horadam sequence and some perturbed tridiagonal 2-Toeplitz matrices: A unified approach. [PDF]

Heliyon, 2022
Anđelić M, da Fonseca CM, Yılmaz F.
europepmc   +1 more source

A Note on Stability of an Operator Linear Equation of the Second Order

Abstract and Applied Analysis, 2011
We prove some Hyers-Ulam stability results for an operator linear equation of the second order that is patterned on the difference equation, which defines the Lucas sequences (and in particular the Fibonacci numbers).
Janusz Brzdȩk, Soon-Mo Jung
doaj   +1 more source