Results 41 to 50 of about 1,912,276 (202)
On (k,p)-Fibonacci numbers and matrices [PDF]
Notes on Number Theory and Discrete MathematicsIn 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 +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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Counting the sum of cubes for Lucas and Gibonacci numbers
Science and Technology Indonesia, 2019 Lucas and Gibonacci numbers are two sequences of numbers derived from a welknown numbers, Fibonacci numbers. The difference between Lucas and Fibonacci numbers only lies on the first and second elements.
Wamiliana Wamiliana +2 more
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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
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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.
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Generalized Hybrid Fibonacci and Lucas p-numbers
, 2022 The hybrid numbers are a generalization of complex, hyperbolic and dual numbers. Until this time, many researchers have studied related to hybrid numbers.
Kocer, E. Gokcen, Alsan, Huriye
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Some new identities for the sum of generalized Fibonacci numbers and generalized Lucas numbers [PDF]
Mathematica MoravicaLet UN and Vn denote the n-th generalized Fibonacci and generalized Lucas numbers, respectively. In this paper, we calculate the n-th powers of some square matrices by diagonalizing them with their eigenvalues and eigenvectors.
Lıman Gülsüm +2 more
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SOME CONNECTIONS BETWEEN THE SMARANDACHE FUNCTION AND THE FIBONACCI SEQUENCE [PDF]
, 2013 This paper is aimed to provide generalizations of the Smarandache function. They will be constructed by means of sequences more general than the sequence of the factorials.
Dunutrescu, C., Rocsoreanu, C.
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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 +2 more
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