\begin{definition}[Definition:Fibonacci-Like Sequence]
Let $A = \tuple {a_0, a_1, \ldots, a_{n - 1} }$ be an ordered tuple of numbers.
The '''Fibonacci-like sequence formed from $A$''' is defined as:
:$\map {F_A} k = \begin {cases} \qquad \qquad a_k & : 0 \le k < n \\
& \\ \ds \sum_{k - n \mathop \le j \mathop < k} a_j & : k \ge n \end {cases}$
That is, apart from the first $n$  terms, every term is the sum of the previous $n$ terms.
The main term can also be expressed as:
:$\map {F_A} k = 2 \map {F_A} {k - 1} - \map {F_A} {k - n}$
\end{definition}