Non-homogenous recurrence relation I need to solve the recurrence relation  $A(n)=2A(n-2)+ 2^{n-2}$. I tried writing out equations up to the $A(2)$ and multiplying by powers of two and adding all the equations together  then all the terms cancelled but after that I couldn't find the sum of the powers of two. I forgot to mention that the base is $A(2)=2$ and n is even

Let us compute some values of A(n):
$n=2, A(2)=2$
$n=4, A(4)=2A(2)+2^2=8=2^3$
$n=6, A(6)=2A(4)+2^4=32=2^5$
$n=8, A(8)=2A(6)+2^6=128=2^7$
You should see the pattern, It seems that $A(n)=2^{n-1}$. This is true and can be easily shown by induction.
