\begin{definition}[Definition:Linear Recurrence Relation]
A '''linear recurrence relation''' is a recurrence relation which has the form:
:$a_n y_{n+k} + a_{n-1} y_{n+k-1} + \cdots + a_0 y_k = b \left({k}\right)$
where $a_0, \ldots, a_n$ are constants.
\end{definition}