I am taking a summer class in discrete math and have done very well up till now. I am nervous because I have reviewed the lecture slides and practice problems but I still don't really understand what to do. The problem example I was given is:
Suppose $f$ is defined by:
\begin{align} f(0) &= 0, \\ f(1) &= 1, \\ f(n + 2) &= f(n + 1) + 2\times f(n) \end{align}
Question: Find $f(2), f(3), f(4), f(5), f(6)$
Now I understand that what I am doing is finding the function by plugging in the previous function, but I do not understand the $f(n+2)$. How do I interpret this? Does this mean that for $f(2)$ I plug in the result of $f(1)$ and add $2$ to it? Or do I plug in $0$ since $0+2 = 2$ and I am trying to find $f(2)$?