OBM 2012 Problem 1

In a culturing of bacteria, there are two species of them: red and blue bacteria.

When two red bacteria meet, they transform into one blue bacterium. When two blue bacteria meet, they transform into four red bacteria. When a red and a blue bacteria meet, they transform into three red bacteria.

Find, in function of the amount of blue bacteria and the red bacteria initially in the culturing, all possible amounts of bacteria, and for every possible amount, the possible amounts of red and blue bacteria.