Check out these numbers and you will see that every one is divisible by 3 with a remainder of 1. So write out the sequence, subtracting 1 from each:
3, 12, 27, 48, 75.
If we divide each by 3 we get:
1, 4, 9, 16, 25. But these are the squares of the natural numbers 1, 2, 3, 4, 5.
Hence the formula: 3n²+1.