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International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 64 | Number 1 | Year 2018 | Article Id. IJMTT-V64P509 | DOI : https://doi.org/10.14445/22315373/IJMTT-V64P509

Binomial Transforms of Generalized Fibonacci-Like Sequences


Yasemin Taşyurdu
Abstract

In this study, we apply binomial transforms to generalized Fibonacci-Like sequences associated with Fibonacci and Lucas sequences. We obtain the Binet formulas and generating functions of these transforms. Also, we introduce an infinite triangle consist of the terms of generalized Fibonacci-Like sequences and their binomial transforms.

Keywords
Fibonacci sequence, Lucas sequences, Binomial Transforms, Binet Formulo
References

[1] P. Bhadouria, D. Jhala and B. Singh, “Binomial Transforms of the k-Lucas Sequences and its Properties,” Journal of Mathematics and Computer Science, vol. 8, pp. 81-92, 2014.
[2] S. Falcon and A. Plaza, “Binomial Transforms of the k-Fibonacci Sequence,” International Journal of Nonlinear and Numerical Simulation, vol. 10(11-12), pp. 1527-1538, 2009.
[3] Y. K. Gupta, M. Singh and O. Sikhwall, “GeneralizedFibonacci-LikeSequenceAssociatedwithFibonacciandLucasSequences,” Turkish Journal of Analysis and Number Theory, vol. 2(6), pp. 233-238, 2014.
[4] S. Harne, B. Singh, and S. Pal, “Generalized Fibonacci-like sequence and Fibonacci sequence,” Int. J. Contemp. Math. Sci. vol. 9(5),pp. 235-241, 2014.
[5] T. Koshy, “Fibonacci and Lucas Numbers with Applications,” John Wiley and SonsInc, NY, 2001.
[6] H. Prodinger, “Some information about the binomial transform,” The Fibonacci Quarterly, vol. 32(5), pp. 412-415, 1994.
[7] M.Z. Spivey and L. L. Steil, “The k-binomial transform and the Hankel transform,” Journal Integer Sequences, vol. 9, 2006.

Citation :

Yasemin Taşyurdu, "Binomial Transforms of Generalized Fibonacci-Like Sequences," International Journal of Mathematics Trends and Technology (IJMTT), vol. 64, no. 1, pp. 59-64, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V64P509

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