In[1]:=
S[n_] := Piecewise[{{0, Mod[n, 4] == 1 }, {20*30^(n/2 - 1),
     Mod[n, 2] == 0}, {100*500^((n - 3)/4), Mod[n, 4] == 3}}];
Sum[S[k], {k, 1, 9}]

Out[1]= 608720