How can I get all the situations of ki, which subjects to the equation？

i is an varied integer from 1 to N (N is a given integer i.e. 40). ki is also an integer, whose value can be any one from -3 to 3. I want to calculate all the different combinations of ki subjecting to the condition that sigma(i*ki)=n. (n is a varied integer with a value from 1 to N). For example, we let n=20, the answers for this equation should include ki=1(i=20), ki=0(i≠20); and ki=2(i=10), ki=0(i≠10) etc.