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Sign Enumeration
What is the number of solutions of $(a_i)_{i=1}^n$ such that
$$\sum_{i=1}^nia_i\le b,\quad a_i\in\{-1,1\},\quad \sum_{i=1}^n{a_i}=c$$
given $b,c\in\mathbf Z$?
Is there a generating function solution?
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