How to solve with constants A and B when I have $a_0=0$ and $a_1=1$?

Question

I have an issue. As a result, I have $a_n = A \, 2^n + B \, (-1)^n$. The post is from here:

recursive equation with a

How to continue to the solution?

What I did was to take $a_0 = A \, 2^0 + B \, (-1)^0$.

Answer 1

Hint: For $n=0$ you will get $$a_0=A+B=0$$ And for $n=1$ we get $$a_1=2A-B=1$$

Adding both equation you will get $$3A=1$$