Results 51 to 60 of about 187 (159)

On repdigits as product of $k$-Fibonacci and $k$-Lucas numbers [PDF]

Mathematica Bohemica
For an integer $k\geq2$, let $(F_n^{(k)})_{n\geq-(k-2)}$, $(L_n^{(k)})_{n \geq-(k-2)}$ be $k$-Fibonacci and $k$-Lucas sequences, respectively. For these sequences the first $k$ terms are $0,\ldots,0,1$ and $0,\ldots,0,2,1$, respectively, and each term ...
Safia Seffah, Salah Eddine Rihane, Alain Togbé   +2 more
doaj   +1 more source

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

Construction of helices from Lucas and Fibonacci sequences

, 2017
By means of two complex-valued functions (depending on an integer parameter P>=1) we construct helices of integer ratio R>=1 related to the so-called Binet formulae for P-Lucas and P-Fibonacci sequences. Based on these functions a new map is defined and we show that its three-dimensional representation is also a helix.
openaire   +2 more sources

The sequences of Fibonacci and Lucas for quadratic fields

Boletim da Sociedade Paranaense de Matemática
We construct the sequences of Fibonacci and Lucas in any quadratic field $\mathbb{Q}(\sqrt{d}\,)$ with $d>0$ square free, noting that the general properties remain valid as those given by the classical sequences of Fibonacci and Lucas for the case $d = 5$, under the respective variants.
Pablo Lam-Estrada, Myrian Rosalia Maldonado-Ramirez, Jose Luis Lopez-Bonilla, Fausto Jarquin Zarate, R. Rajendra, Siva Kota Reddy Polaepalli   +5 more
openaire   +1 more source

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

Verbena officinalis Verbenaceae (Lamiales): a new plant model system for phyllotaxis research. [PDF]

J Plant Res, 2021
Zagórska-Marek B, Turzańska M, Chmiel K.   +2 more
europepmc   +1 more source

A combined approach to Perrin and Padovan hybrid sequences. [PDF]

Heliyon, 2021
Jafari Petroudi SH, Pirouz M, Karaca E, Yılmaz F.   +3 more
europepmc   +1 more source