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
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $1 \cdotp 83928 \, 67552 \, 1416 \ldots$