Fibonacci Sequence recursion algorithm and the time complexity
You can prove that $T(n) \geq F_n$ by induction. For $n = 0$ and $n = 1$ we have $T(n) \geq 1$ and $F_n \leq 1$. Suppose that the claim holds for $n-1$ and $n-2$. Then
$$
T(n) = T(n-1)+T(n-2)+3 \geq F(n-1)+F(n-2) = F(n).
$$