The sequence of trifurcating Fibonacci numbers

Parimalkumar A. Patel, Dr. Devbhadra V. Shah

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.

Keywords


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

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References


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DOI: http://dx.doi.org/10.23755/rm.v41i0.668

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