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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

  1. Atanassov, K T., Atanassov V., Shannon A. and Turner J., 2002. New Visual Perspective On Fibonacci Number, World Scientific Publishing Company, Singapore.
  2. Atanassov, K.T., Hlebarova, J. and Mihov, S., 1992. Recurrent formulas of the generalized Fibonacci and Tribonacci sequence, The Fibonacci Quarterly, Vol.30, No. 1, 77-79.
  3. Atanassov, K.T., 1986. On a generalization of the Fibonacci sequence in the case of three sequences, The Fibonacci Quarterly, Vol. 27, No. 1, 7-10.
  4. Atanassov, K. T., 1995. Remark on a New Direction for a Generalization of the Fibonacci Sequence, The Fibonacci Quarterly, Vol. 33, No. 3, 249-250.
  5. Hope, P., 1995. Exponential Growth of Random Fibonacci Sequences, The Fibonacci Quarterly, Vol. 33, No. 2, 164-168.
  6. Glaister, P., 1994. Multiplicative Fibonacci Sequences, The Mathematical Gazette, Vol. 78, No. 481, 68.
  7. Lee, J. Z., Lee, J. S., 1987. Some Properties of the Generalization of the Fibonacci Sequence, The Fibonacci Quarterly, Vol. 25, No.2, 111-117.
  8. Rathore G. P. S., Jain. S. and Sikhwal, O., 2012. Multiplicative Coupled Fibonacci Sequences of third Order, International Journal of Contemporary Mathematical Sciences, Vol. 7, No. 31, 1535 – 1540.
  9. Rathore, G. P. S., Sikhwal, O. and Jain, S., 2012. Generalized Coupled Fibonacci Sequences, International Journal of Computer Application , Vol. 59, No.8, 12-15.
  10. Singh, B., Sikhwal, O., Jain S., 2010. Coupled Fibonacci Sequence of Fifth Order and Some Properties, International Journal of Mathematical Analysis, Vol. 4, No. 25, 1247-1254.
  11. Singh, B. and Sikhwal, O., 2010. Multiplicative Coupled Fibonacci Sequences and Some Fundamental Properties, International Journal of Contemporary Mathematical Sciences, Vol. 5, No. 5, 223-230.

Keywords

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