I recently took a look a project euler, and I am trying to think of a smart way to do number 2. I looked at the sequence, and I saw that the question is basically asking for
$$
\sum\_{i=1}^n F\_{3i}
$$

For whatever n is gives me the nth even under a million. So, I did some fiddling around with this, and I got this to be equivalent to

$$
\sum\_{i=0}^{n-1} F\_{3i-1}(3^{n-i}-1)
$$

I was wondering, is there even a closed form for something like this? Or am I wasting my time? I couldn't find a closed form online anywhere.