How do I find the number of ways to represent a number as a sum of only $1$’s and $2$’s and $3$’s?
I think the title is self-explanatory.
E.g., if I have to represent $13$ as a sum of only $1$'s and $2$'s, or $1$'s, $2$'s and $3$'s, what will the formula for finding the number of unordered ways this can be done, i.e., $2 + 2 + 1 = 2 + 1 + 2$?
I'm sorry if this is an easy question, but it's been a long time since I used any permutations and combinations, and it's all hazy.
P.S. Can you tell me a good online resource to brush up advanced permutations and combinations?