Math. J. Interdiscip. Sci.

Fibonacci and k Lucas Sequences as Series of Fractions

A. D. Godase and M. B. Dhakne

KEYWORDS

k -Fibonacci sequence, k -Lucas sequence, Recurrence relation

PUBLISHED DATE March 2016
PUBLISHER The Author(s) 2015. This article is published with open access at www.chitkara.edu.in/publications
ABSTRACT

In this paper, we defined new relationship between k Fibonacci and k Lucas sequences using continued fractions and series of fractions, this approach is different and never tried in k Fibonacci sequence literature.

Page(s) 107–119
URL http://dspace.chitkara.edu.in/jspui/bitstream/1/686/1/42009_MJIS_Godse.pdf
ISSN Print : 2278-9561, Online : 2278-957X
DOI 10.15415/mjis.2016.42009
REFERENCES
  • A. D. Godase, M. B. Dhakne, On the properties of k Fibonacci and k Lucas numbers , International Journal of Advances in Applied Mathematics and Mechanics, 02 (2014), 100 - 106.
  • A. D. Godase, M. B. Dhakne, Fundamental Properties of Multiplicative Coupled Fibonacci Sequences of Fourth Order Under Two Specific Schemes , International Journal of Mathematical Archive , 04, No. 6 (2013), 74 - 81.
  • A. D. Godase, M. B. Dhakne, Recurrent Formulas of The Generalized Fibonacci Sequences of Fifth Order ,"International Journal of Mathematical Archive" , 04, No. 6 (2013), 61 - 67.
  • A. D. Godase, M. B. Dhakne, Summation Identities for k Fibonacci and k Lucas Numbers using Matrix Methods, "International Journal of Mathematics and Scientific Computing" , 05, No. 2 (2015), 75 - 78.
  • A. D. Godase, M. B. Dhakne, Determinantal Identities for k Lucas Sequence,"Journal of New Theory" , 12 (2016), 01 - 07.
  • A. F. Horadam, Basic Properties of a Certain Generalized Sequence of Numbers , The Fibonacci Quarterly, 03, No. 3 (1965), 161 - 176.
  • Sergio Falcon, Angel Plaza, On the k Fibonacci numbers , Chaos, Solitons and Fractals, 32 , No. 05 (2007), 1615 - 1624.
  • Sergio Falcon, Angel Plaza, The k Fibonacci sequence and the Pascal 2-triangle , Chaos, Solitons and Fractals, 33, No. 1 (2007), 38 - 49.
  • Sergio Falcon, Angel Plaza, The k-Fibonacci hyperbolic functions , Chaos, Solitons and Fractals Vol. 38, No.2 (2008), 409 - 420.
  • Piero Filipponi, Alwyn F. Horadam, A Matrix Approach to Certain Identities , The Fibonacci Quarterly, 26, No. 2 (1988), 115 - 126.
  • H. W. Gould, A History of the Fibonacci Q-Matrix and a Higher-Dimensional Problem , The Fibonacci Quarterly , 19, No. 3 (1981), 250 - 257.
  • A. F. Horadam, Jacobsthal Representation of Polynomials , The Fibonacci Quarterly, 35, No. 2 (1997) 137 - 148.
  • Thomas Koshy, Fibonacci and Lucas numbers with applications , Wiley - Intersection Publication (2001).
  • N. J. Sloane, The on-line encyclopedia of integer sequences 2012.
  • Gilbert Strang, Introduction to Linear Algebra , Wellesley - Cambridge Press (2003).
  • Steven Vajda, Fibonacci and Lucas numbers and the Golden Section: Theory and applications , Ellis Horwood Ltd., (1989).
  • Marcellus E. Waddill , Matrices and Generalized Fibonacci Sequences , The Fibonacci Quarterly, 12, No. 4 (1974) 381 - 386