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Sorry in advance if this is not the right place to ask this simple question.

As it is usual, $A_n ={ (a_1,\dots,a_{n+1}) \in\mathbb Z^{n+1}:a_1+\dots+a_{n+1}=0}$. Now we define the norm $$\|(a_1,\dots,a_{n+1})\|:= \sum_{i:a_i>0} a_i.$$ I would like an algorithm with input $(n,k)$, that returns all elements in $A_n$ with norm equal to $k$.

Sorry in advance if this is not the right place to ask this simple question.

As it is usual, $A_n ={ (a_1,\dots,a_{n+1}) \in\mathbb Z^{n+1}:a_1+\dots+a_{n+1}=0}$. Now we define the norm $$\|(a_1,\dots,a_{n+1})\|:= \sum_{i:a_i>0} a_i.$$ I would like an algorithm with input $(n,k)$, that returns all elements in $A_n$ with norm equal to $k$.