Bash Me Not

Since it follows the Fibonacci recurrence relation, then the general formula would be in the form of $g_{n}=a(\frac{1+\sqrt{5}}{2})^n + b(\frac{1-\sqrt{5}}{2})^n$ Now the first two terms given represent: $a+b=2$ $a(\frac{1+\sqrt{5}}{2})+b(\frac{1-\sqrt{5}}{2})=-1$ Solving this system, we get: $a=(\frac{\sqrt{5}-2}{\sqrt{5}}) ~and ~b=(\frac{\sqrt{5}+2}{\sqrt{5}})$ Thus, the formula for $g_{n}$ is $g_{n}=(\frac{\sqrt{5}-2}{\sqrt{5}})(\frac{1+\sqrt{5}}{2})^n + (\frac{\sqrt{5}+2}{\sqrt{5}})(\frac{1-\sqrt{5}}{2})^n$ Using Wolfram, we get the last two digits $\implies \boxed{13}$