# Recurrence relation over a finite alphabet

Let $$A_n$$ be the set of all finite words over the alphabet $$\{1,2,3\}$$ whose digits sum to $$n$$. I am trying to find a recurrence relation with initial conditions for $$|A_n|$$. I have checked the first few $$n$$ and got that $$|A_1|=1$$ , $$|A_2|=2$$, $$|A_3|=4$$, $$|A_4|=7$$, $$|A_5|=13$$, $$|A_6|=24$$. I can't seem to find a pattern that allows me to create a recurrence relation, nor I am I sure how I could check that such a pattern would be correct.