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Fibonacci and k Lucas Sequences as Series of Fractions

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.


  • A. D. Godase, V. P. College, Vaijapur, Maharashtra, India
  • M. B. Dhakne, Dr. B.A.M. University, Aurangabad, Maharashtra, India


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



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.

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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.

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