\[\begin{align*} o_i^{(k)} &= q_i^{(k - 1)} \left(z_i^{(k)} + z_{i \mod 3 + 1}^{(k)}\right) + q_{i \mod 3 + 1}^{(k - 1)} \left(z_i^{(k)} \right) \\ q_i^{(k)} &= o_i^{(k - 1)} \left( o_i^{(k - 1)} + 2o_{i \mod 3 + 1}^{(k - 1)} \right) \\ z_i^{(k)} &= p_i^{(k)} \left( p_i^{(k)} + 2p_{(i + 1) \mod 3 + 1}^{(k)} \right) \\ q_i^{(0)} &= p_i^{(0)} \left( p_i^{(0)} + 2p_{(i + 1) \mod 3 + 1}^{(0)} \right) = z_i^{(0)} \\ p_i^{(k)} &= p_i^{(k - 1)} \left( p_i^{(k - 1)} + 2p_{i \mod 3 + 1}^{(k - 1)} \right) \end{align*}\]
\[\begin{align*} p_1^{(0)} &= \epsilon \\ p_2^{(0)} &= 1 - 2 \epsilon \\ p_3^{(0)} &= \epsilon \\ \\ p_1^{(1)} &= - 3 \epsilon^{2} + 2 \epsilon \\ p_2^{(1)} &= 1 - 2 \epsilon \\ p_3^{(1)} &= 3 \epsilon^{2} \\ \end{align*}\]
\[\begin{align*} z_1^{(0)} &= 3 \epsilon^{2} \\ z_2^{(0)} &= 1 - 2 \epsilon \\ z_3^{(0)} &= - 3 \epsilon^{2} + 2 \epsilon \\ \\ z_1^{(1)} &= - 9 \epsilon^{4} + 4 \epsilon^{2} \\ z_2^{(1)} &= 12 \epsilon^{3} - 10 \epsilon^{2} + 1 \\ z_3^{(1)} &= 9 \epsilon^{4} - 12 \epsilon^{3} + 6 \epsilon^{2} \\ \end{align*}\]
\[\begin{align*} q_1^{(0)} &= 3 \epsilon^{2} \\ q_2^{(0)} &= 1 - 2 \epsilon \\ q_3^{(0)} &= - 3 \epsilon^{2} + 2 \epsilon \\ \\ o_1^{(1)} &= 9 \epsilon^{4} - 12 \epsilon^{3} + 6 \epsilon^{2} \\ o_2^{(1)} &= 12 \epsilon^{3} - 10 \epsilon^{2} + 1 \\ o_3^{(1)} &= - 9 \epsilon^{4} + 4 \epsilon^{2} \\ \\ q_1^{(1)} &= - 81 \epsilon^{8} + 108 \epsilon^{7} - 162 \epsilon^{6} + 192 \epsilon^{5} - 76 \epsilon^{4} - 12 \epsilon^{3} + 10 \epsilon^{2} \\ q_2^{(1)} &= 12 \epsilon^{3} - 10 \epsilon^{2} + 1 \\ q_3^{(1)} &= 81 \epsilon^{8} - 108 \epsilon^{7} + 162 \epsilon^{6} - 192 \epsilon^{5} + 76 \epsilon^{4} \\ \end{align*}\]