Negative Forever

Let $c$ be a real number. The sequence $a_1, a_2, a_3, ...$ is defined by $a_1 = c$ and $a_n= 2 a_{n-1}^2 -1$ for all $n \geq 2$ . Find the sum of $c$ such that $a_n < 0$ for all $n \geq 1.$

This problem is not original.