\[a_{1} = 2;\ \ a_{2} = 1;\ \ \]
\[a_{n + 2} = 3a_{n} + a_{n + 1}^{2}\]
\[a_{3} = 3 \cdot 2 + 1^{2} = 7;\]
\[a_{4} = 3 \cdot 1 + 7^{2} = 49 + 3 = 52.\]