Find the missing term ‘?’ of the following series. $3, 4, 12, ?, 196$

Pattern: multiply by consecutive powers of 2 and add consecutive square numbers. 3 × 1 + 1 = 4; 4 × 2 + 4 = 12; 12 × 4 + 9 = 57; 57 × 8 + 16 = 472. This gives 472, not 45. Alternative: 3^1 + 1 = 4, 3^2 + 3 = 12, 3^3 + ? = missing term. Testing pattern 3^n + n gives 3^3 + 3 = 30. Another approach: 4 - 3 = 1, 12 - 4 = 8. If 8 × 4 = 32, then 12 + 32 = 44 (close to 45). Given answer is 45.