What are the next three numbers in the pattern 3 9 12 21 33 54?

The next three numbers are: 87, 141, 228.

Each number in the sequence after the first two is the sum of the previous two numbers. This is a variation of the Fibonacci sequence which starts with 1, 1, ... (and then continues ..., 2, 3, 5, 8, 13, ...).