$$G(x) = [G(x-1)+G(x-2)]^2\\ G(0) = 0,\quad G(1) = 1$$
$$Q(x) = [Q(x-1)]^2 + [Q(x-2)]^2\\ Q(0) = 0,\quad Q(1) = 1$$
$$P(x) = G(x) + Q(x)$$ What is the sum of the digits of $P(29)$? I am unable to solve this problem. I got an answer, but I think it was wrong.