On the Fibonacci k-numbers

Falcón, Sergio; Plaza, Ángel

doi:10.1016/j.chaos.2006.09.022

Cited by 256 publications

(186 citation statements)

References 32 publications

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“…The well-known Binet formula in the Fibonacci numbers theory [5,3,1] allows us to express the k-Fibonacci and the kLucas numbers by mean of the roots As a result of the above,…”

Section: Definition Of the K-fibonacci Numbersmentioning

confidence: 99%

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Some new formulas on the K-Fibonacci numbers

Falcón

2018

JAM

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I S S N 2 3 4 7 -1 9 2 1 V o l u m e 1 4 N u m b e r 1 J o u r n a l o f A d v a n c e s i n M a t h e m a t i c s 7439 | P a g e J a n u a r y 2 0 1 8 w w w . c i r w o r l d . c o m SOME NEW FORMULAS ON THE K-FIBONACCI NUMBERS Sergio FalconDepatment of Mathematics University of Las Palmas de Gran Canaria (Spain) sergio.falcon@ulpgc.es ABSTRACT In this paper, we find some formulas for finding some special sums of the k-Fibonacci or the k-Lucas numbers. We find also some formulas that relate the k-Fibonacci or the k--Lucas numbers to some sums of these numbers..

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“…The well-known Binet formula in the Fibonacci numbers theory [5,3,1] allows us to express the k-Fibonacci and the kLucas numbers by mean of the roots As a result of the above,…”

Section: Definition Of the K-fibonacci Numbersmentioning

confidence: 99%

“…There exist generalizations of the classical Fibonacci numbers given by many researchers as Horadam [4] and recently by Falcon and Plaza [3].…”

Section: Introductionmentioning

confidence: 99%

Some new formulas on the K-Fibonacci numbers

Falcón

2018

JAM

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“…Falcon and Plaza [1] showed some results of the k-Fibonacci sequence   k,n Then many researchers [3][4][5] showed some results of the k-Fibonacci-Like number in 2014.…”

Section: Introductionmentioning

confidence: 99%

Some properties of the generalized (p,q)- Fibonacci-Like number

Suvarnamani

2018

MATEC Web Conf.

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“…The k−Fibonacci sequence introduced by Falcon and Plaza [3] depends only on one integer parameter k and is de ned as F k, = , F k, = and F k,n+ = kF k,n + F k,n− , where n ≥ , k ≥ . In particular, if k = , the Pell sequence is obtained as P = , P = and P n+ = Pn +P n− for n ≥ .…”

Section: Introductionmentioning

confidence: 99%

Laplace - Fibonacci transform by the solution of second order generalized difference equation

Pinelas

Xavier

Kumar

et al. 2017

Nonautonomous Dynamical Systems

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Abstract:The main objective of this paper is nding new types of discrete transforms with tuning factor t. This is not only analogy to the continuous Laplace transform but gives discrete Laplace-Fibonacci transform (LF t ). This type of Laplace-Fibonacci transform is not available in the continuous case. The LF t generates uncountably many outcomes when the parameter t varies on ( , ∞). This possibility is not available in the existing Laplace transform. All the formulae and results derived are veri ed by MATLAB.

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On the Fibonacci k-numbers

Cited by 256 publications

References 32 publications

Some new formulas on the K-Fibonacci numbers

Some new formulas on the K-Fibonacci numbers

Some properties of the generalized (p,q)- Fibonacci-Like number

Laplace - Fibonacci transform by the solution of second order generalized difference equation

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