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International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 51 | Number 2 | Year 2017 | Article Id. IJMTT-V51P518 | DOI : https://doi.org/10.14445/22315373/IJMTT-V51P518

On Some identities for Generalized (k, r) Fibonacci Numbers


Ashwini Panwar, Kiran Sisodiya, G.P.S. Rathore
Abstract

We have formulated Binet`s formula for Generalized (k, r) Fibonacci numbers. Also we have obtained some identities, including generating function for (k, r) Fibonacci sequence.

Keywords
(k, r) Fibonacci numbers, Binet`s formula, Generating function, recurrence relation.
References

[1] D. Brod, K. Piejko and I. Wloch, Distance Fibonacci numbers, distance Lucas numbers and their applications, Ars Combinatoria, CXII(2013), 397- 410.
[2] I. Wloch, U. Bednarz, D. Brod, A. Wloch and M. Wolowiecz-Musial, On a new type of distance Fibonacci numbers, Discrete Applied Mathematics, 161(2013), 2695-2701.
[3] S. Falcon and A. Plaza, On the Fibonacci k-numbers, Chaos, Solitons &Fractals, 32(5) (2007), 1615-24.
[4] S. Falcon and A. Plaza, The k-Fibonacci sequence and the Pascal 2- triangle, Chaos, Solit. & Fract., 33(1) (2007), 38-49.
[5] S. Falcon and A. Plaza, On k-Fibonacci numbers of arithmetic indexes, Applied Mathematics and Computation, 208(2009), 180-185.
[6] S. Falcon, Generalized (k, r) – Fibonacci number, Gen. Math. Notes, 25(2)(2014), 148-158.
[7] Y.K. Gupta, K. Sisodiya, M. Singh, Generaliation of Fibonacci sequence and related properties, Research Journal of Computation and Mathematics 3(2)(2015).

Citation :

Ashwini Panwar, Kiran Sisodiya, G.P.S. Rathore, "On Some identities for Generalized (k, r) Fibonacci Numbers," International Journal of Mathematics Trends and Technology (IJMTT), vol. 51, no. 2, pp. 146-148, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V51P518

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