This is a homework question so specifically I am looking for a direction (help). Not an absolute answer.
I understand how to solve 2nd order nonhomogeneous (and I think 3rd order is similiar) recurrence relations. Whats kinking me up with this one is a term with n.
h[n] = 4h[n- 1] - 4h[n-2] + 3n + 1
Here I am using square brackets to indicate subscripts. Now I can reorganize this equation into:
0 = h[n] - 4h[n-1] + 4h[n-2] -3n-1
From which I can derive the characteristic equation:
0 = x^3 - 4x^2 + 4x - 3n -1
Normally at this point I would solve the roots and be on my way, but here I have that extra n. How do I deal with this?