Fibonacci and k Lucas Sequences as Series of Fractions.
DOI:
https://doi.org/10.15415/mjis.2016.42009Keywords:
k -Fibonacci sequence, k -Lucas sequence, Recurrence relationAbstract
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.
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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 MathematicalArchive", 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 (2015), 01 - 07.
A. F. Horadam, Basic Properties of a Certain Generalized Sequence of Numbers, The Fibonacci Quarterly, 03, No. 3 (1965), 61 - 76.
S. Falcon, A. Plaza, On the k Fibonacci numbers, Chaos, Solitons and Fractals, 05, No. 32 (2007), 1615 - 1624.
S. Falcon, A. Plaza, The k Fibonacci sequence and the Pascal 2 triangle, Chaos, Solitons and Fractals, 33, No. 1 (2007), 38 - 49.
S. Falcon, A. Plaza, The k Fibonacci hyperbolic functions, Chaos, Solitons and FractalsVol. 38, No.2 (2008), 409 - 20.
P. Filipponi,A. 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 - 57.
A. F. Horadam, Jacobstal Representation of Polynomials, The Fibonacci Quarterly, 35, No. 2 (1997) 137 - 148.
T. Koshy, Fibonacci and Lucas numbers with applications, Wiley - Intersection Publication (2001).
N. J. Sloane, The on-line encyclopedia of integer sequences 2006.
G. Strang, Introduction to Linear Algebra, Wellesley - Cambridge: Wellesley, M.A. Publication (2003).
S. Vajda, Fibonacci and Lucas numbers and the Golden Section: Theory and applications, Chichester: Ellis Horwood, (1989).
M. E. Waddill, Matrices and Generalized Fibonacci Sequences, The Fibonacci Quarterly, 55, No. 12 (1974) 381 - 386.
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Mathematical Journal of Interdisciplinary Sciences by Chitkara University Publications is licensed under a Creative Commons Attribution 4.0 International License. Based on a work at https://mjis.chitkara.edu.in |