How can I get number of combinations with given sum?

For example in vector [3,2,2,2,1,1,1,1,1] and given sum 4 the result should be counted like

• 5 choose 4 possibilities to choose 4 ones (1+1+1+1=4)
• (3 choose 1)*(5 choose 2) possibilities to choose 1 two and 2 ones (2+1+1=4)
• 3 choose 2 possibilities to choose 2 twos (2+2=4)
• (1 choose 1)*(5 choose 1) possibilities to choose 1 three and 1 one (3+1=4)

So the number of combinations is (5 choose 4)+(3 choose 1)*(5 choose 2)+(3 choose 2)+(1 choose 1)*(5 choose 1)=5+3*10+3+1*5=43 if I didn't do any mistake.

But I don't know how to write this algorithm to matlab so I use brute force and just generate all combinations with one element, then all combinations with two elements etc. and then for all combinations find ouf if their sum is equal to given number. So in these comninations are for example 30 combinations [2,1,1]. But I want faster algorithm which find only one time combination [1,1,1,1] and then use nchoosek to count, how many possibilities are there to get 4 ones of 5. Then find [2,1,1] and count again number of possibilities (30) etc. Can anyone help me?