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venn diagram questions

For a given (n,m,k)..

Using values in the range (0..k), how many different m-combos can be made which sum to n?

For example, if (n,m,k) = (3,3,2) there are 7 possible combinations. For (5,4,2) there seem to be 16.

I've been trying to approach this like the binomial formula, stars and bars sort of deal but the k-constraint is puzzling me and I'm not entirely sure of what to do.

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