Akm[k_,m_]:=Piecewise[{{0, (k != 3 && (k != 1 || m != 0)) || (m != -2 && m != 0 && m != 2)}, {A[1, 0], k == 1 && m == 0}, {A[3, 2], k == 3 && (m == -2 || m == 2)}}, A[3, 0]]