# Math Help - Recurrance Relation

1. ## Recurrance Relation

I have asked to solve the linear non-homogeneous equation.

$A(n) = 8A(n-2) -16A(n-4) +F(n) , where F(n) = N^2*4^n$

All these n are subscript of A.

I am not sure how to resolve that F(n).

Can anyone help me.

2. Using a well known theorem and taking into account that $4$ is not a root of the charactheristic equation, a particular
solution for the complete equation has the form $X(x)=(an^2+bn+c)4^n$.

3. Can you please name the theorem used.

4. If $F(n)=a^nP_m(n)$ where $P_m(n)$ is a polynomial of degree $m$, and $a$ is not a root of the characteristic equation, then a particular solution for the complete is $x(n)=a^nQ_m(n)$, where $Q_m(n)$ is a polynomial of degree $m$. If $a$ is a root of the characteristic equation with multiplicity $s$ then, $x(n)=a^mn^sQ_m(n)$.

Regards.