Let [math]S_{n} = n^{2} + 20n + 12[/math], where [math]n[/math] is a positive integer. What is the sum of all possible values of n for which [math]S_{n}[/math] is a perfect square? Given [math]S_n = n^2 +20n + 12[/math]. What will be the sum of positive integers such that [math]S_n[/math] will be a perfect square?