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<math>
 
<math>
 
   \begin{align}
 
   \begin{align}
F(P,A) =    \begin{cases}
+
G(a_1, , a_p) =    \begin{cases}
\binom{P+A-1}{A-1}     &, A < P \\
+
a_1 + 1    &, p=1 \\
\sum_{i=1}^{P-1} \binom{A}{i}\binom{P-1}{i-1}  + \binom{A}{P} &, A \ge P
+
F(a_p, p) + G(a_1,..,a_{p-1}) &, p \ne 1
 
\end{cases}
 
\end{cases}
 
   \end{align}
 
   \end{align}
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