Linear recurrence
A sequence 
is said to obey a linear recurrence of order 
if there exist constants 
such that ![\[a_{n+k} = \sum_{i=0}^{k-1}c_{i}a_{n+i}\]](http://latex.artofproblemsolving.com/6/1/c/61cc4c8799017be3f17608de04c3da6bc37468ca.png)
for all 
.
There is a systematic way of solving linear recurrences, found in the page Characteristic Equation.
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