Some properties and extended Binet’s formula for the class of bifurcating Fibonacci sequence

Authors

  • Daksha Manojbhai Diwan Government Engineering College,Gandhinagar.
  • Devbhadra V Shah Veer Narmad South Gujarat University, SURAT
  • Vandana R Patel Sir , P.T.Science College, Modasa

DOI:

https://doi.org/10.23755/rm.v51i0.1293

Keywords:

Fibonacci sequence, bifurcating Fibonacci sequence, generalization of Fibonacci sequence, Binet formula

Abstract

One of the generalizations of Fibonacci sequence is a -Fibonacci sequence, which is further generalized in several other ways, some by conserving the initial conditions and others by conserving the related recurrence relation. In this paper, we generalize the sequence of -Fibonacci numbers into the sequence of bifurcating Fibonacci numbers. The Binet-like formula for the terms of these numbers is obtained and further, we obtain several interesting properties related to the sequence.

 

References

De Villiers, M., A Fibonacci generalization and its dual, International Journal of Mathematics Education, Science and Technology, 31, (2000), 464 – 473.

Diwan D. M., Shah D. V. Explicit and recursive formulae for the class of generalized Fibonacci sequence. International Journal of Advanced Research in Engineering, Science and Management. 1 (10), 1 – 6, July 2015.

Diwan D. M., Shah D. V. Extended Binet’s formula for the class of generalized Fibonacci sequences. VNSGU Journal of Science and Technology. 4 (1), 205 – 210, 2015.

Diwan Daksha M., Shah Devbhadra V.: Extended Binet’s formula for the class of generalized Fibonacci sequences, Proceeding of 19th Annual Cum 4th International conference of Gwalior Academy of Mathematical Sciences, (2014), 109 – 113.

Falcon S., A simple proof of an interesting Fibonacci generalization, International Journal of Mathematics Education, Science and Technology, 35 (2), (2004), 259 – 261.

Falcon S., Plaza, A: On the Fibonacci K-numbers, Chaos, Solitons & Fractals, 32 (5), (2007), 1615 – 1624.

Falcon S., Plaza, A.: On the 3-dimensional k-Fibonacci spirals, Chaos, Solitons & Fractals, 38 (4), (2008), 993 – 1003.

Falcon S., Plaza, A: The k-Fibonacci hyperbolic functions, Chaos Solitons & Fractals, 38 (4), (2008), 409 – 420.

Falcon S., Plaza, A: The k-Fibonacci sequence and Pascal 2-triangle, Chaos, Solitons & Fractals, (33) (1), (2007), 38 – 49.

Koshy Thomas: Fibonacci and Lucas Numbers with applications, John Wiley and Sons, Inc., N. York, 2001.

Marcia Edson, Omer Yayenie: A new generalization of Fibonacci sequence and extended Binet’s formula, Integers, 9 (6), (2009), 639 – 654.

Verma, Ankur Bala. On Properties of generalized Bi-variate Bi-Periodic Fibonacci polynomials. International journal of Advanced science and Technology. 29 (3), 8065 – 8072, 2020.

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Published

2024-01-31

Issue

Vol. 51 (2024)

Section

Volume 51-2024

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