Turkish Journal of Analysis and Number Theory
ISSN (Print): 2333-1100 ISSN (Online): 2333-1232 Website: http://www.sciepub.com/journal/tjant
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Turkish Journal of Analysis and Number Theory. 2014, 2(1), 9-12
DOI: 10.12691/tjant-2-1-3
Open AccessArticle

On the k-Fibonacci-Like Numbers

Yashwant K. Panwar1, , G. P. S. Rathore2 and Richa Chawla3

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

2Department of Mathematical Sciences, College of Horticulture, Mandsaur, India

3School of Studies in Mathematics, Vikram University, Ujjain, India

Pub. Date: February 11, 2014

Cite this paper:
Yashwant K. Panwar, G. P. S. Rathore and Richa Chawla. On the k-Fibonacci-Like Numbers. Turkish Journal of Analysis and Number Theory. 2014; 2(1):9-12. doi: 10.12691/tjant-2-1-3

Abstract

The Fibonacci number is famous for possessing wonderful and amazing properties. In this study, we introduce the k-Fibonacci-Like number and related identities. We establish some of the interesting properties of k-Fibonacci-Like number. We shall use the Induction method and Binet’s formula for derivation.

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

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References:

[1]  A. F. Horadam, Basic Properties of Certain Generalized Sequence of Numbers, The Fibonacci Quarterly, 3(3) (1965), 161-176.
 
[2]  A. F. Horadam, The Generalized Fibonacci Sequences, The American Math. Monthly, 68(5) (1961), 455-459.
 
[3]  A. J. Macfarlane, Use of Determinants to present identities involving Fibonacci and Related Numbers, The Fibonacci Quarterly, 48(1) (2010), 68-76.
 
[4]  A. T. Benjamin and J. J. Quinn, Recounting Fibonacci and Lucas identities, College Math. J., 30(5) (1999), 359-366.
 
[5]  B. Singh, O. Sikhwal, and S. Bhatnagar, Fibonacci-Like Sequence and its Properties, Int. J. Contemp. Math. Sciences, 5(18) (2010), 859-868.
 
[6]  B. Singh, V. K. Gupta, and Y. K. Panwar, On Combinations of Higher Powers of Fibonacci-Like sequence, Open Journal of Mathematical Modeling, 1 (2), (2013), 63-66.
 
[7]  D. Kalman and R. Mena, The Fibonacci Numbers – Exposed, The Mathematical Magazine, 2 (2002).
 
[8]  L. A. G. Dresel, Transformations of Fibonacci-Lucas identities, Applications of Fibonacci Numbers, 5 (1993), 169-184.
 
[9]  L. R. Natividad, Deriving a Formula in Solving Fibonacci-like sequence, International Journal of Mathematics and Scientific Computing, 1(1) (2011), 19-21.
 
[10]  N. N. Vorobyov, The Fibonacci numbers, D. C. Health and company, Boston, 1963.
 
[11]  S. Falco´n, On the k-Lucas numbers. International Journal of Contemporary Mathematical Sciences, 6(21) (2011), 1039-1050.
 
[12]  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.
 
[13]  S. Falco´n, Plaza, A.: On the Fibonacci k-numbers. Chaos, Solitons & Fractals, 32(5) (2007), 1615-1624.
 
[14]  S. Falco´n, Plaza, A.: The k-Fibonacci hyperbolic functions. Chaos, Solitons & Fractals, 38(2) (2008), 409–420.
 
[15]  S. Falco´n, Plaza, A.: The k-Fibonacci sequence and the Pascal 2-triangle. Chaos, Solitons &Fractals, 33(1) (2007), 38-49.
 
[16]  S. Vajda, Fibonacci and Lucas numbers, and the golden section. Theory and applications. Chichester: Ellis Horwood limited (1989).
 
[17]  T. Koshy, Fibonacci and Lucas numbers with Applications, Wiley, 2001.
 
[18]  V. K. Gupta, Y. K. Panwar and N. Gupta, identities of Fibonacci-Like sequence, J. Math. Comput. Sci. 2(6) (2012), 1801-1807.
 
[19]  V. K. Gupta, Y. K. Panwar and O. Sikhwal, Generalized Fibonacci Sequences, Theoretical Mathematics & Applications, 2(2) (2012), 115-124.