The sequence of trifurcating Fibonacci numbers

Authors

  • Parimalkumar A. Patel Department of Mathematics, Veer Narmad South Gujarat University, Surat - 395007.
  • Dr. Devbhadra V. Shah Department of Mathematics, Veer Narmad South Gujarat University, Surat - 395007.

DOI:

https://doi.org/10.23755/rm.v41i0.668

Keywords:

Fibonacci sequence, bifurcating Fibonacci sequence, generalization of Fibonacci sequence, Binet formula, identities related with the Fibonacci sequence.

Abstract

One of the interesting generalizations of Fibonacci sequence is a k-Fibonacci sequence, which is further generalized into the ‘Bifurcating Fibonacci sequence’. In this paper we further generalize it into the sequence of ‘trifurcating Fibonacci numbers’. We obtain the Binet-like formula for these numbers. We also obtain the analogous of Cassini’s identity, Catalan’s identity, d’Ocagne’s identity and some fundamental identities for the terms of this sequence.

References

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Published

2021-12-31

Issue

Vol. 41 (2021)

Section

Volume 41-2021

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