Which function should I use to solve the sum of the varied integer product?

I want to get all the possible combinations of ki which subject to the equation that sigma(i*ki)=10. i is an integer from 1 to 10; ki is also an integer with a value varied from -3 to 3. For example, ki=1 for i=10 and ki=0 for i≠10. This is only one situation. Another situation is that ki=2 for i=5, ki=0 for i≠5 etc. Integer linear programming seems to be not suitable to this situation. Which function should be used to solve this problem? Thanks