Results 51 to 60 of about 976 (217)

On (k,p)-Fibonacci numbers and matrices [PDF]

Notes on Number Theory and Discrete Mathematics
In this paper, some relations between the powers of any matrices X satisfying the equation Xᵏ-pXᵏ⁻¹-(p-1)X-I=0 and (k,p)-Fibonacci numbers are established with ...
Sinan Karakaya, Halim Özdemir, Tuğba Demirkol   +2 more
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On the bounds for the spectral norms of geometric circulant matrices

Journal of Inequalities and Applications, 2016
In this paper, we define a geometric circulant matrix whose entries are the generalized Fibonacci numbers and hyperharmonic Fibonacci numbers. Then we give upper and lower bounds for the spectral norms of these matrices.
Can Kızılateş, Naim Tuglu
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On Generalized Jacobsthal and Jacobsthal–Lucas Numbers

Annales Mathematicae Silesianae, 2022
Jacobsthal numbers and Jacobsthal–Lucas numbers are some of the most studied special integer sequences related to the Fibonacci numbers. In this study, we introduce one parameter generalizations of Jacobsthal numbers and Jacobsthal–Lucas numbers.
Bród Dorota, Michalski Adrian
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On $k$-Fibonacci balancing and $k$-Fibonacci Lucas-balancing numbers

Karpatsʹkì Matematičnì Publìkacìï, 2021
The balancing number $n$ and the balancer $r$ are solution of the Diophantine equation $$1+2+\cdots+(n-1) = (n+1)+(n+2)+\cdots+(n+r). $$ It is well known that if $n$ is balancing number, then $8n^2 + 1$ is a perfect square and its positive square root is
S.E. Rihane
doaj   +1 more source

On hyper-dual generalized Fibonacci numbers [PDF]

, 2020
In this paper, we define hyper-dual generalized Fibonacci numbers.
ÖMÜR, NEŞE, KOPARAL, SİBEL
core   +1 more source

On Generalized Fibonacci Numbers [PDF]

The American Mathematical Monthly, 1971
(1971). On Generalized Fibonacci Numbers. The American Mathematical Monthly: Vol. 78, No. 10, pp. 1108-1109.
openaire   +1 more source

Bi-Periodic (p,q)-Fibonacci and Bi-Periodic (p,q)-Lucas Sequences

Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 2023
In this paper, we define bi-periodic (p,q)-Fibonacci and bi-periodic (p,q)-Lucas sequences, which generalize Fibonacci type, Lucas type, bi-periodic Fibonacci type and bi-periodic Lucas type sequences, using recurrence relations of (p,q)-Fibonacci and (p,
Yasemin Taşyurdu, Naime Şeyda Türkoğlu   +1 more
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Using Generalized Fibonacci Sequences for Solving the One-Dimensional LQR Problem and its Discrete-Time Riccati Equation [PDF]

Modeling, Identification and Control, 2010
In this article we develop a method of solving general one-dimensional Linear Quadratic Regulator (LQR) problems in optimal control theory, using a generalized form of Fibonacci numbers.
Per-Ole Nyman, Lars Petter Lystad, Johan Byström   +2 more
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Generalized Hyper-Fibonacci Numbers and Applications

, 2022
\textit{Hyper-Fibonacci numbers} were first defined by \textit{A. Dil} and \textit{I. Mező} [Appl. Math. Comput. 206, No. 2, 942--951 (2008; Zbl 1200.65104)]. The goal of the paper under review is to (i) provide some combinatorial properties of a generalization of the \textit{hyper-Fibonacci numbers}, and (ii) to apply these properties to the \textit ...
Ait-Amrane, Lyes, Behloul, Djilali
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Restricted Permutations, Fibonacci Numbers, and k-generalized Fibonacci Numbers

, 2002
A permutation $π\in S_n$ is said to {\it avoid} a permutation $σ\in S_k$ whenever $π$ contains no subsequence with all of the same pairwise comparisons as $σ$. For any set $R$ of permutations, we write $S_n(R)$ to denote the set of permutations in $S_n$ which avoid every permutation in $R$.
Egge, Eric S., Mansour, Toufik
openaire   +3 more sources