Finding the Big-O and Big-Omega bounds of a program
$1.6180^n$ is not an upper bound to the running time of your program, not even up to multiplicative constants (in fact it is a lower bound).
However $O(\phi^n)$ is a valid upper bound, where $\phi = \frac{1+\sqrt{5}}{2} &gt; 1.618$ is the golden ratio. It is also easy to see that your program takes $\Omega(\phi^n)$ time, so the above upper bound is asymptotically tight.
That said, $\phi^n \not\in O(n^2)$, so that answer is incorrect.
Moreover, $\phi^n \not\in \Omega(e^n)$ since $\phi &lt; e$, so that answer is incorrect too.
Finally, notice that your answers contradict each other since you say that the running time of the program is both in $\Omega(e^n)$ and in $O(n^2)$ but $\Omega(e^n) \cap O(n^2) = \emptyset$.