Solving for the closed term solution of a third order recurrence relation with real constant coefficients

Solving for the closed term solution of a third order recurrence relation
with real constant coefficients

How would you solve for the closed term form of $a(n)$ given the general
form of the third order linear homogenous recurrence relation with real
constant coefficients.
$a(n)-P\,a(n-1)-Q\,a(n-2)-R\,a(n-3)=0$
with the initial terms of a1, a2, and a3
and given that the roots of the characteristic equations have
two repeated roots and a real root
three repeated roots
(can you give answers for both cases please)
For second order recurrence relations I know that you can use generating
functions to deduce a closed form because it is then expressed as a
arithmetic series which can be converted into a closed form.
However in the case of the general term of the third order recurrence
relations if I follow the same steps what I did with the second order
recurrence relation, instead of getting a simple arithmetic series I
seemed to get a second order recurrence relation inside the series.
What am I doing wrong?
or is there a different method of approach in this case?
Please help