Nice one! I was unaware of this property of the Fibonacci sequence, but after examining it makes sense because adding two odds will always produce an even, and adding an even and an odd always produces an odd, so the sequence of (even, odd, odd) will repeat every forever.
It’s also possible to calculate the n-th Fibonacci number directly using the golden ratio, phi. So for this case, we can just calculate every 3rd number since we know they are even.