I have the difference equation:

$x\_{n+2} - \frac{1}{2}x\_{n+1} + \frac{1}{8}x\_{n} = \cos(\frac{n\pi}{2})$

I am guessing the special solution is on the form:

$A\cos(\frac{n\pi}{2}) + B\sin(\frac{n\pi}{2})$

I haven't encountered an equation on this form before, I am used to special solutions on the form of say:

$An + B$

Any tips on how to procede?