k-Generalized Fibonacci Numbers

Yashwant K. Panwar^1, and Mamta Singh²

¹Department of Mathematics and MCA, Mandsaur Institute of Technology, Mandsaur, India

²Department of Mathematical Sciences and Computer Application, Bundelkhand University, Jhansi (U. P.), India

Cite this paper:
Yashwant K. Panwar and Mamta Singh. k-Generalized Fibonacci Numbers. Applied Mathematics and Physics. 2014; 2(1):10-12. doi: 10.12691/amp-2-1-3

Abstract

In this paper, we present the k-Generalized Fibonacci sequence. This sequence generalizes other, Generalized Fibonacci sequence. Generalized Fibonacci sequence was introduced by Gupta, Panwar and Sikhwal in 2012. We establish some of the interesting properties of k- Generalized Fibonacci sequence.

Keywords:
Generalized Fibonacci numbers k-Generalized Fibonacci numbers Binet’s formula

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References:

[1]	A. F. Horadam, A generalized Fibonacci sequence. Math Mag., 68 (1961), 455-459.
[2]	Hoggatt, V.E., Fibonacci and Lucas numbers. Palo Alto, CA: Houghton, (1969).
[3]	Hoggatt, V.E. Jr., Phillips, J.W. and Leonard, H. Jr., “Twenty-four Master Identities”, The Fibonacci Quarterly, Vol.9, No.1, (1971), 1-17.
[4]	S. Falco´n, On the k-Lucas numbers. International Journal of Contemporary Mathematical Sciences, 6 (21) (2011), 1039-1050.
[5]	S. Falco´n, On the Lucas Triangle and its Relationship with the k-Lucas numbers. Journal of Mathematical and Computational Science, 2 (3) (2012), 425-434.
[6]	S. Falco´n, Plaza, A.: On the Fibonacci k-numbers. Chaos, Solitons & Fractals, 32 (5) (2007), 1615-1624.
[7]	S. Falco´n, Plaza, A.: The k-Fibonacci hyperbolic functions. Chaos, Solitons & Fractals, 38 (2) (2008), 409-20.
[8]	S. Falco´n, Plaza, A.: The k-Fibonacci sequence and the Pascal 2-triangle. Chaos, Solitons & Fractals, 33 (1) (2007), 38-49.
[9]	S. Vajda, Fibonacci and Lucas numbers, and the golden section. Theory and applications. Chichester: Ellis Horwood limited (1989).
[10]	T. Koshy, Fibonacci and Lucas Numbers with Applications, John Wiley, New York. (2001).
[11]	V. K. Gupta and Y. K. Panwar “Common factors of generalized Fibonacci, Jacobstha and Jacobsthal-Lucas numbers”, International Journal of Applied Mathematica Research, Vol.1, No.4 (2012), 377-382.
[12]	V. K. Gupta, Y. K. Panwar and O. Sikhwal, “Generalized Fibonacci sequences” Theoretical Mathematics & Applications, Vol.2, No.2 (2012), 115-124.