Linear recurrence

A sequence $\{a_{0},a_{1},a_{2},\ldots\}$ is said to obey a linear recurrence of order $k$ if there exist constants $c_{0},c_{1},\ldots,c_{k-1}$ such that $a_{n+k} = \sum_{i=0}^{k-1}c_{i}a_{n+i}$ for all $n \ge 0$ .