I am trying to find the solution to the following recurrence relation:
$$a_n - 6a_{n-1} + 12a_{n-2} - 8a_{n-3} = n2^n; a_0 = 1, a_1 = 2, a_2 = 6$$
Solving the homogeneous part is simple, but how do I determine the particular solution. Is is:
$$a^p_n = An^42^n$$ I have chosen this because the characteristic equation of the homogeneous part to be:
$$(x -2)^3 = 0$$ Now solved some equations like this one before, since the root is $2$ with multiplicity $3$, I have chosen the particular solution to be $a^p_n = A (n^3)n2^n$
Am I correct?