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S_3=5,25,61,113,181,\cdots\\  S_4=7,88,337,850,1723, \cdots\\  S_5=11,311,1863,6395,1640, \cdots  \end{equation}  We can then find the sequence function for each of these sequences, for example \begin{equation}  S_1(n)=2\\  S_2(n)=4n-1\\  S_3(n)=8n^2-4n+1\\  S_4(n)=16n^3-12n^2+5n-2\\  S_5(n)=32n^4-32n^3+18n^2-10n+3\\  \end{equation}