1

$\alpha =0$

$\begin{array}{l}\left\{\begin{array}{cc}1& \begin{array}{cc}7& \begin{array}{cc}12& 6\end{array}\end{array}\end{array}\right\}\\ \odot \left\{\begin{array}{cc}\left(\begin{array}{c}n\\ n\end{array}\right)& \begin{array}{cc}\left(\begin{array}{c}n\\ n-1\end{array}\right)& \begin{array}{cc}\left(\begin{array}{c}n\\ n-2\end{array}\right)& \begin{array}{cc}\left(\begin{array}{c}n\\ n-3\end{array}\right)& \begin{array}{cc}\left(\begin{array}{c}n\\ n-4\end{array}\right)& \left(\begin{array}{c}n\\ n-5\end{array}\right)\end{array}\end{array}\end{array}\end{array}\end{array}\right\}\\ =\left\{\stackrel{\text{ParentSequence}}{\overbrace{\begin{array}{cc}1& \begin{array}{cc}8& \begin{array}{cc}27& \begin{array}{cc}64& \begin{array}{cc}125& \begin{array}{cc}216& \begin{array}{cc}343& \cdots \end{array}\end{array}\end{array}\end{array}\end{array}\end{array}\end{array}}}\right\}\end{array}$

2

$\alpha =1$

$\stackrel{\text{DirectProductRule}}{\overbrace{\left\{\begin{array}{cc}1& \begin{array}{cc}6& 6\end{array}\end{array}\right\}\odot \left\{\begin{array}{cc}\left(\begin{array}{c}n\\ n-1\end{array}\right)& \begin{array}{cc}\left(\begin{array}{c}n\\ n-2\end{array}\right)& \left(\begin{array}{c}n\\ n-3\end{array}\right)\end{array}\end{array}\right\}}}$

$\left\{\begin{array}{cc}1& \begin{array}{cc}8& \begin{array}{cc}27& \begin{array}{cc}64& \begin{array}{cc}125& \begin{array}{cc}216& \begin{array}{cc}343& \cdots \end{array}\end{array}\end{array}\end{array}\end{array}\end{array}\end{array}\right\}\oplus$

3

$\alpha =2$

$\left\{\begin{array}{cc}1& \begin{array}{cc}5& 1\end{array}\end{array}\right\}\odot \left\{\begin{array}{cc}\left(\begin{array}{c}n+1\\ n-1\end{array}\right)& \begin{array}{cc}\left(\begin{array}{c}n+1\\ n-2\end{array}\right)& \left(\begin{array}{c}n\\ n-3\end{array}\right)\end{array}\end{array}\right\}=\left\{\begin{array}{cc}1& \begin{array}{cc}8& \begin{array}{cc}27& \begin{array}{cc}64& \cdots \end{array}\end{array}\end{array}\end{array}\right\}$

4

$\alpha =3$

$\begin{array}{l}\left\{\begin{array}{cc}1& \begin{array}{cc}4& 1\end{array}\end{array}\right\}\odot \left\{\begin{array}{cc}\left(\begin{array}{c}n+2\\ n-1\end{array}\right)& \begin{array}{cc}\left(\begin{array}{c}n+1\\ n-2\end{array}\right)& \left(\begin{array}{c}n\\ n-3\end{array}\right)\end{array}\end{array}\right\}\\ =\left\{\begin{array}{cc}1& \begin{array}{cc}8& \begin{array}{cc}27& \begin{array}{cc}64& \begin{array}{cc}125& \begin{array}{cc}216& \begin{array}{cc}343& \cdots \end{array}\end{array}\end{array}\end{array}\end{array}\end{array}\end{array}\right\}\end{array}$

5

$Ker$

No direct product is carried out on the kernels before priming

6

$\alpha =4$

$\begin{array}{l}\left\{\begin{array}{cc}1& \begin{array}{cc}3& \begin{array}{cc}-3& -1\end{array}\end{array}\end{array}\right\}\odot \left\{\begin{array}{cc}\left(\begin{array}{c}n+3\\ n-1\end{array}\right)& \begin{array}{cc}\left(\begin{array}{c}n+2\\ n-2\end{array}\right)& \begin{array}{cc}\left(\begin{array}{c}n+1\\ n-3\end{array}\right)& \left(\begin{array}{c}n\\ n-4\end{array}\right)\end{array}\end{array}\end{array}\right\}\\ =\left\{\begin{array}{cc}1& \begin{array}{cc}8& \begin{array}{cc}27& \begin{array}{cc}64& \begin{array}{cc}125& \begin{array}{cc}216& \begin{array}{cc}343& \cdots \end{array}\end{array}\end{array}\end{array}\end{array}\end{array}\end{array}\right\}\end{array}$