Definition:Tribonacci Sequence/General

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 $a = 0, b = 0, c = 1$.