For a second-order recurrence $a_n = c_1 a_{n-1} + c_2 a_{n-2}$ with characteristic roots $r_1 = 2$ and $r_2 = -3$, what are the coefficients $c_1$ and $c_2$? (Use Vieta's formulas: $r_1 + r_2 = c_1$ and $r_1 \cdot r_2 = -c_2$.)