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

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.

Keywords

• fibonacci sequence, bifurcating fibonacci sequence, generalization of fibonacci sequence, binet formula