# Definition:Linear Recurrence Relation

## Definition

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**.