Additive Pulsating Fibonacci Sequences and Some Results

Volume 1, Issue 1, October 2016     |     PP. 149-160      |     PDF (314 K)    |     Pub. Date: November 23, 2016
DOI:    401 Downloads     8261 Views  

Author(s)

Shikha Bhatnagar, School of Studies in Mathematics, Vikram University Ujjain (M. P.), India
Omprakash Sikhwal, School of Studies in Mathematics, Vikram University Ujjain (M. P.), India

Abstract
In this paper, we consider additive pulsating Fibonacci sequences. First, we are introduced additive pulsating Fibonacci sequences of first and second kind. Further, explicit formulas in the form of its members are formulated and proved for additive pulsating Fibonacci sequences of first and second kind.

Keywords
Fibonacci Sequence, Additive Pulsating Fibonacci Sequences

Cite this paper
Shikha Bhatnagar, Omprakash Sikhwal, Additive Pulsating Fibonacci Sequences and Some Results , SCIREA Journal of Mathematics. Volume 1, Issue 1, October 2016 | PP. 149-160.

References

[ 1 ] A. F. Horadam, A generalized Fibonacci sequence”, Amer. Math. Monthly, vol. 68, no.5, pp 455-459, 1961.
[ 2 ] A. F. Horadam, Basic properties of certain generalized sequence of numbers, The Fibonacci Quarterly, 3(3) (1965),161-176.
[ 3 ] A. Suvarnamani, S. Koyram, Multiplicative Pulsated Fibonacci Sequences Part 2, Universal Journal of Applied Mathematics. 3(5) (2015), 89-93.
[ 4 ] J. Z. Lee and J. S. Lee, Some properties of the generalization of the Fibonacci sequence, The Fibonacci Quarterly, 25(2) (1987), 111-117.
[ 5 ] K. T. Atanassov, L. C. Atanassov, D. D. Sasselov, A New Perspective to the Generalization of the Fibonacci Sequence, The Fibonacci Quarterly. 23(1) (1985), 21-28.
[ 6 ] K. T. Atanassov, On a Second New Generalization of the Fibonacci Sequence, The Fibonacci Quarterly. 24(4) (1986), 362-365.
[ 7 ] K. T. Atanassov, Pulsating Fibonacci sequences, Notes on Number Theory and Discrete Mathematics. 19(3) (2013), 12–14.
[ 8 ] K. T. Atanassov, Remark on a New Direction for a Generalization of the Fibonacci Sequence, The Fibonacci Quarterly. 33(3) (1995), 249-250.
[ 9 ] K. T. Atanassov, , V. Atanassov, A. G. Shannon, J. C. Turner, New Visual Perspectives on Fibonacci Numbers, World Scientific Publishing Company, Singapore. (2002).
[ 10 ] M. Singh M., O. Sikhwal., S. Jain, Coupled Fibonacci sequences of fifth order and some properties, International Journal of Mathematical Analysis, 4(25) (2010),1247-1254.
[ 11 ] O. Sikhwal, Generalization of Fibonacci sequence: An intriguing sequence, Lap Lambert Academic, Publishing GmbH & Co. KG, Germany. (2012).