A recurrence [[Relation]] for some [[Sequence]] $\set{a_{n}}$ is an equation that expresses $a_{n}$ in terms of one or more of its previous terms in the [[Sequence]] $(a_{0},a_{1},\dots,a_{n-1}) \forall n : n > n_{0}$, where $n_{0}\in\Z^+$. The opposite of this would be to describe a sequence with a [[Sequence|Closed Form]] equation where $a_n$ is expressed without using any other term in the [[Sequence]]. A [[Sequence]] is called a solution of the [[Recurrence Relation]] if its terms satisfy the [[Recurrence Relation]]. >[!example] >Let $a_n$ be the sequence defined by the [[Recurrence Relation]]: >$\large >a_{n} = na_{n-1} + a_{n-2}^2 >$ >$\large \underbrace{a_{0} = -1, a_{1}=0}_{\text{Initial Conditions}} $