Definition:Linear Recurrence Relation

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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.

Homogeneous Linear Recurrence Relation

If in a linear recurrence relation $b \left({k}\right) = 0$, then the equation is homogeneous.

Otherwise it is inhomogeneous.