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Generalized Multiplicative Coupled Fibonacci Sequence and its Properties

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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 158 - Number 10
Year of Publication: 2017
Authors:
Omprakash Sikhwal, Yashwant Vyas, Shikha Bhatnagar
10.5120/ijca2017912838

Omprakash Sikhwal, Yashwant Vyas and Shikha Bhatnagar. Generalized Multiplicative Coupled Fibonacci Sequence and its Properties. International Journal of Computer Applications 158(10):14-17, January 2017. BibTeX

@article{10.5120/ijca2017912838,
	author = {Omprakash Sikhwal and Yashwant Vyas and Shikha Bhatnagar},
	title = {Generalized Multiplicative Coupled Fibonacci Sequence and its Properties},
	journal = {International Journal of Computer Applications},
	issue_date = {January 2017},
	volume = {158},
	number = {10},
	month = {Jan},
	year = {2017},
	issn = {0975-8887},
	pages = {14-17},
	numpages = {4},
	url = {http://www.ijcaonline.org/archives/volume158/number10/26941-2017912838},
	doi = {10.5120/ijca2017912838},
	publisher = {Foundation of Computer Science (FCS), NY, USA},
	address = {New York, USA}
}

Abstract

The coupled Fibonacci sequences are new direction of generalization of Fibonacci sequence. The concept of coupled Fibonacci sequence was first introduced by Atanassov, K. T. in 1985. He deliberated multiplicative coupled Fibonacci sequences of second order in 1995. Multiplicative coupled Fibonacci sequences are less known and popularized now days. Generalized Multiplicative Coupled Fibonacci sequences of second order are defined by the recurrence relations αn+2 = pβn+1qβn and βn+2 = rαn+1sαn, n ≥ 0 with initial conditions α0 = a, β0 = b, α1 = c, β1 = d where p q, r and s are real numbers. In this paper, sum identities of generalized multiplicative coupled Fibonacci sequences of second order are presented and derived.

References

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Keywords

Coupled Fibonacci sequences, Multiplicative coupled Fibonacci sequences, Generalized Coupled Fibonacci Sequences