I have the following difference equation: $y[n]=y[n-2]-0.25y[n-4]+x[n]-x[n-2]$ I need to find the first 6 values of the impulse response of the system characterized by that equation. When I do that, the values I get are: $[1,0,0,0,-0.25,0]$, starting from index zero. I have the answer, which states that the right response is $[1,0,0,0,-0.25,1]$. I really cannot find my mistake; any help will be appreciated.
Answers in textbooks are not necessarily right.. I have got the same answer as you ;)
If you are not sure that your method is right, you can always test digital systems on your PC (matlab, scilab, python, octave, or almost in any language )