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I am new to mathematica and I want to create the set of all n-tuples whose sum is less than a fixed number $N$. My idea would be to do a for loop where I choose first number $k_1$ in between 0 and N, then I choose my second number in between 0 and $N-k_1$, etc... At each step I have to check that $N-k_1-\dots-k_i\neq0$. If it is, the loop should break, the rest of the k's should be set to $0$ and the loop should restart. Is there anyway to code this efficiently in mathematica? Thus far, my only idea is to do Select[Tuples[Range[0, N], n], Sum[#] <= order &], which is highly inefficient.

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