In how many ways one can decompose an integer $n$ to smaller integers at least 3? for example 13 has the following decompositions:
\begin{gather*} 13\\ 3,10\\ 4,9\\ 5,8\\ 6,7\\ 3,3,7\\ 3,4,6\\ 3,5,5\\ 3,3,3,4\\ 4,4,5\\ \end{gather*}
Points and hints are welcome.