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Generalized Multiplicative Coupled Fibonacci Sequence and its Properties
| 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, Shikha Bhatnagar . Generalized Multiplicative Coupled Fibonacci Sequence and its Properties. International Journal of Computer Applications. 158, 10 ( Jan 2017), 14-17. DOI=10.5120/ijca2017912838
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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