Definition:Tribonacci Sequence/General

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Definition

A general Tribonacci sequence is a sequence $\left \langle {u_n}\right \rangle$ which is formally defined recursively as:

$u_n = \begin{cases} a & : n = 0 \\ b & : n = 1 \\ c & : n = 2 \\ u_{n - 1} + u_{n - 2} + u_{n - 3} & : n > 2 \end{cases}$

where $a, b, c \in \Z$ are constants.


It is usual to define the Tribonacci sequence as a general Tribonacci sequence with $a = 0, b = 0, c = 1$.


Also see

  • Results about Tribonacci sequences can be found here.


Linguistic Note

The word Tribonacci, in the context of Tribonacci constant and Tribonacci sequence, is a portmanteau word formed from tri, from the Greek word for three, and the name of the mathematician Fibonacci.

Hence it is pronounced trib-bo-nat-chi, or trib-bo-nar-chi, according to taste.

The word arises as a direct analogy with the Fibonacci numbers.


Sources