I was given a sequence (0, 0, 1, 2, 4, 8, 16). I am tasked with finding the generating function. So far I have reached this point: A(x) = x^2 + 2x^3 + 4x^4 + 8x^5 + 16x^6 + ... -xA(x) = x^2 + x^3 + x^4 + x^5 + x^6 + ...
A(x) - xA(x) = x^3 + 3x^4 + 7x^5 + 15x^6 Any input on where to go from here would be appreciated.
Well, like I mentioned in my comment, you have a geometric series. You can find the formula here. Basically, you were on the right track, but the ratio between terms is $2x$. Try multiplying $A(x)$ by $2x$ and subtracting.