1

${\mathcal{A}}_{-1}$ $a=-1$

$\begin{array}{l}\left\{\stackrel{\text{ParentSequence}}{\overbrace{\begin{array}{cc}0& \begin{array}{cc}8& \begin{array}{cc}27& \begin{array}{cc}64& \begin{array}{cc}125& \begin{array}{cc}216& \begin{array}{cc}343& \cdots \end{array}\end{array}\end{array}\end{array}\end{array}\end{array}\end{array}}}\right\}\\ \oplus \left\{\begin{array}{ccccccc}\left(\begin{array}{c}-0\\ 0\end{array}\right)& \left(\begin{array}{c}-1\\ 0\end{array}\right)& \left(\begin{array}{c}-2\\ 0\end{array}\right)& \left(\begin{array}{c}-3\\ 0\end{array}\right)& \left(\begin{array}{c}-4\\ 0\end{array}\right)& \left(\begin{array}{c}-4\\ 0\end{array}\right)& \\ & \left(\begin{array}{c}-1\\ 1\end{array}\right)& \left(\begin{array}{c}-2\\ 1\end{array}\right)& \left(\begin{array}{c}-3\\ 1\end{array}\right)& \left(\begin{array}{c}-4\\ 1\end{array}\right)& \left(\begin{array}{c}-4\\ 1\end{array}\right)& \\ & & \left(\begin{array}{c}-2\\ 2\end{array}\right)& \left(\begin{array}{c}-3\\ 2\end{array}\right)& \left(\begin{array}{c}-4\\ 2\end{array}\right)& \left(\begin{array}{c}-4\\ 2\end{array}\right)& \cdots \\ & & & \left(\begin{array}{c}-3\\ 3\end{array}\right)& \left(\begin{array}{c}-4\\ 3\end{array}\right)& \left(\begin{array}{c}-4\\ 3\end{array}\right)& \\ & & & & \left(\begin{array}{c}-4\\ 4\end{array}\right)& \left(\begin{array}{c}-4\\ 4\end{array}\right)& \end{array}\right\}=\left\{\begin{array}{cc}8& \begin{array}{cc}19& \begin{array}{cc}18& 6\end{array}\end{array}\end{array}\right\}\end{array}$

2

${\mathcal{A}}_0$

$a=0$

$\begin{array}{l}\left\{\stackrel{\text{ParentSequence}}{\overbrace{\begin{array}{cc}1& \begin{array}{cc}8& \begin{array}{cc}27& \begin{array}{cc}64& \begin{array}{cc}125& \begin{array}{cc}216& \begin{array}{cc}343& \cdots \end{array}\end{array}\end{array}\end{array}\end{array}\end{array}\end{array}}}\right\}\\ \oplus \left\{\begin{array}{ccccccc}\left(\begin{array}{c}-0\\ 0\end{array}\right)& \left(\begin{array}{c}-1\\ 0\end{array}\right)& \left(\begin{array}{c}-2\\ 0\end{array}\right)& \left(\begin{array}{c}-3\\ 0\end{array}\right)& \left(\begin{array}{c}-4\\ 0\end{array}\right)& \left(\begin{array}{c}-4\\ 0\end{array}\right)& \\ & \left(\begin{array}{c}-1\\ 1\end{array}\right)& \left(\begin{array}{c}-2\\ 1\end{array}\right)& \left(\begin{array}{c}-3\\ 1\end{array}\right)& \left(\begin{array}{c}-4\\ 1\end{array}\right)& \left(\begin{array}{c}-4\\ 1\end{array}\right)& \\ & & \left(\begin{array}{c}-2\\ 2\end{array}\right)& \left(\begin{array}{c}-3\\ 2\end{array}\right)& \left(\begin{array}{c}-4\\ 2\end{array}\right)& \left(\begin{array}{c}-4\\ 2\end{array}\right)& \cdots \\ & & & \left(\begin{array}{c}-3\\ 3\end{array}\right)& \left(\begin{array}{c}-4\\ 3\end{array}\right)& \left(\begin{array}{c}-4\\ 3\end{array}\right)& \\ & & & & \left(\begin{array}{c}-4\\ 4\end{array}\right)& \left(\begin{array}{c}-4\\ 4\end{array}\right)& \end{array}\right\}=\left\{\begin{array}{cc}1& \begin{array}{cc}7& \begin{array}{cc}12& 6\end{array}\end{array}\end{array}\right\}\end{array}$

3

${\mathcal{A}}_1$ or

${\mathcal{A}}_1$

$\begin{array}{l}\left\{\stackrel{\text{ParentSequence}}{\overbrace{\begin{array}{cc}1& \begin{array}{cc}8& \begin{array}{cc}27& \begin{array}{cc}64& \begin{array}{cc}125& \begin{array}{cc}216& \begin{array}{cc}343& \cdots \end{array}\end{array}\end{array}\end{array}\end{array}\end{array}\end{array}}}\right\}\\ \oplus \left\{\begin{array}{ccccccc}\left(\begin{array}{c}-1\\ 0\end{array}\right)& \left(\begin{array}{c}-2\\ 0\end{array}\right)& \left(\begin{array}{c}-3\\ 0\end{array}\right)& \left(\begin{array}{c}-4\\ 0\end{array}\right)& \left(\begin{array}{c}-4\\ 0\end{array}\right)& \left(\begin{array}{c}-4\\ 0\end{array}\right)& \\ & \left(\begin{array}{c}-2\\ 1\end{array}\right)& \left(\begin{array}{c}-3\\ 1\end{array}\right)& \left(\begin{array}{c}-4\\ 1\end{array}\right)& \left(\begin{array}{c}-4\\ 1\end{array}\right)& \left(\begin{array}{c}-4\\ 1\end{array}\right)& \\ & & \left(\begin{array}{c}-3\\ 2\end{array}\right)& \left(\begin{array}{c}-4\\ 2\end{array}\right)& \left(\begin{array}{c}-4\\ 2\end{array}\right)& \left(\begin{array}{c}-4\\ 2\end{array}\right)& \cdots \\ & & & \left(\begin{array}{c}-4\\ 3\end{array}\right)& \left(\begin{array}{c}-4\\ 3\end{array}\right)& \left(\begin{array}{c}-4\\ 3\end{array}\right)& \\ & & & & \left(\begin{array}{c}-4\\ 4\end{array}\right)& \left(\begin{array}{c}-4\\ 4\end{array}\right)& \end{array}\right\}=\left\{\begin{array}{cc}1& \begin{array}{cc}6& 6\end{array}\end{array}\right\}\end{array}$