A players plays the following game where they roll a die several times successively.

If they roll 1 or 2, they score one point and continue playing. If they roll 3 or 4, they score two points and continue playing. If they roll 5 or 6, they score three points and the game ends.

We call X the total score of the player once the game ends.

1. Compute the probability generating function of X. 2. Give a closed formula for P [X = n]