1 ${\mathbb{B}}_{1}.{\mathbb{B}}_{1}$ $\left\{\begin{array}{cc}1& \begin{array}{cc}6& 1\end{array}\end{array}\right\}\oplus \left\{\begin{array}{cc}\left(\begin{array}{c}n+1\\ n-1\end{array}\right)& \begin{array}{cc}\left(\begin{array}{c}n\\ n-2\end{array}\right)& \left(\begin{array}{c}n-1\\ n-3\end{array}\right)\end{array}\end{array}\right\}$ $\delta =2;\omega =3;g=0$ 2 ${\mathbb{B}}_{1}.{\mathbb{B}}_{2}$ $\left\{\begin{array}{cc}1& \begin{array}{cc}9& \begin{array}{cc}7& -1\end{array}\end{array}\end{array}\right\}\oplus \left\{\begin{array}{cc}\left(\begin{array}{c}n+2\\ n-1\end{array}\right)& \begin{array}{cc}\left(\begin{array}{c}n+1\\ n-2\end{array}\right)& \begin{array}{cc}\left(\begin{array}{c}n\\ n-3\end{array}\right)& \left(\begin{array}{c}n-1\\ n-4\end{array}\right)\end{array}\end{array}\end{array}\right\}$ $\delta =3;\omega =4;g=0$ 3 ${\mathbb{B}}_{1}.{\mathbb{B}}_{3}$ $\left\{\begin{array}{cc}1& \begin{array}{cc}12& \begin{array}{cc}18& \begin{array}{cc}4& -3\end{array}\end{array}\end{array}\end{array}\right\}\oplus \left\{\begin{array}{cc}\left(\begin{array}{c}n+2\\ n-1\end{array}\right)& \begin{array}{cc}\left(\begin{array}{c}n+1\\ n-2\end{array}\right)& \begin{array}{cc}\left(\begin{array}{c}n\\ n-3\end{array}\right)& \begin{array}{cc}\left(\begin{array}{c}n-1\\ n-4\end{array}\right)& \left(\begin{array}{c}n-2\\ n-5\end{array}\right)\end{array}\end{array}\end{array}\end{array}\right\}$ $\delta =4;\omega =5;g=0$ 4 ${\mathbb{B}}_{2}.{\mathbb{B}}_{1}$ $\left\{\begin{array}{cc}1& \begin{array}{cc}9& \begin{array}{cc}7& -1\end{array}\end{array}\end{array}\right\}\oplus \left\{\begin{array}{cc}\left(\begin{array}{c}n+2\\ n-1\end{array}\right)& \begin{array}{cc}\left(\begin{array}{c}n+1\\ n-2\end{array}\right)& \begin{array}{cc}\left(\begin{array}{c}n\\ n-3\end{array}\right)& \left(\begin{array}{c}n-1\\ n-4\end{array}\right)\end{array}\end{array}\end{array}\right\}$ $\delta =3;\omega =4;g=0$ 5 ${\mathbb{B}}_{2}.{\mathbb{B}}_{2}$ $\left\{\begin{array}{cc}1& \begin{array}{cc}13& \begin{array}{cc}19& -1\end{array}\end{array}\end{array}\right\}\oplus \left\{\begin{array}{cc}\left(\begin{array}{c}n+3\\ n-1\end{array}\right)& \begin{array}{cc}\left(\begin{array}{c}n+2\\ n-2\end{array}\right)& \begin{array}{cc}\left(\begin{array}{c}n+1\\ n-3\end{array}\right)& \left(\begin{array}{c}n\\ n-4\end{array}\right)\end{array}\end{array}\end{array}\right\}$ $\delta =4;\omega =4;g=0$ 6 ${\mathbb{B}}_{1}.{\mathbb{B}}_{2}.{\mathbb{B}}_{1}$ $\begin{array}{l}\left\{\begin{array}{cc}1& \begin{array}{cc}32& \begin{array}{cc}62& \begin{array}{cc}0& 1\end{array}\end{array}\end{array}\end{array}\right\}\\ \oplus \left\{\begin{array}{cc}\left(\begin{array}{c}n+3\\ n-1\end{array}\right)& \begin{array}{cc}\left(\begin{array}{c}n+2\\ n-2\end{array}\right)& \begin{array}{cc}\left(\begin{array}{c}n+1\\ n-3\end{array}\right)& \begin{array}{cc}\left(\begin{array}{c}n\\ n-4\end{array}\right)& \left(\begin{array}{c}n-1\\ n-5\end{array}\right)\end{array}\end{array}\end{array}\end{array}\right\}\end{array}$ $\delta =7;\omega =5;g=0$ Trinomial Sequences―Type 4 1 ${\mathbb{T}}_{1}.{\mathbb{T}}_{1}$ $\left\{\begin{array}{cc}1& \begin{array}{cc}6& \begin{array}{cc}12& -1\end{array}\end{array}\end{array}\right\}\oplus \left\{\begin{array}{cc}\left(\begin{array}{c}n+1\\ n-1\end{array}\right)& \begin{array}{cc}\left(\begin{array}{c}n\\ n-2\end{array}\right)& \begin{array}{cc}\left(\begin{array}{c}n-1\\ n-3\end{array}\right)& \left(\begin{array}{c}n-2\\ n-4\end{array}\right)\end{array}\end{array}\end{array}\right\}$ $\delta =2;\omega =4;g=0$ 2 ${\mathbb{T}}_{1}.{\mathbb{T}}_{2}$ $\begin{array}{l}\left\{\begin{array}{cc}1& \begin{array}{cc}9& \begin{array}{cc}27& \begin{array}{cc}17& \begin{array}{cc}6& -6\end{array}\end{array}\end{array}\end{array}\end{array}\right\}\\ \oplus \left\{\begin{array}{cc}\left(\begin{array}{c}n+2\\ n-1\end{array}\right)& \begin{array}{cc}\left(\begin{array}{c}n+1\\ n-2\end{array}\right)& \begin{array}{cc}\left(\begin{array}{c}n\\ n-3\end{array}\right)& \begin{array}{cc}\left(\begin{array}{c}n-1\\ n-4\end{array}\right)& \begin{array}{cc}\left(\begin{array}{c}n-2\\ n-5\end{array}\right)& \left(\begin{array}{c}n-3\\ n-5\end{array}\right)\end{array}\end{array}\end{array}\end{array}\end{array}\right\}\end{array}$ $\delta =3;\omega =6;g=0$ 3 ${\mathbb{T}}_{2}.{\mathbb{T}}_{2}$ $\begin{array}{l}\left\{\begin{array}{cc}1& \begin{array}{cc}13& \begin{array}{cc}55& \begin{array}{cc}71& \begin{array}{cc}41& -19\end{array}\end{array}\end{array}\end{array}\end{array}\right\}\\ \oplus \left\{\begin{array}{cc}\left(\begin{array}{c}n+3\\ n-1\end{array}\right)& \begin{array}{cc}\left(\begin{array}{c}n+2\\ n-2\end{array}\right)& \begin{array}{cc}\left(\begin{array}{c}n+1\\ n-3\end{array}\right)& \begin{array}{cc}\left(\begin{array}{c}n\\ n-4\end{array}\right)& \begin{array}{cc}\left(\begin{array}{c}n-1\\ n-5\end{array}\right)& \left(\begin{array}{c}n-2\\ n-5\end{array}\right)\end{array}\end{array}\end{array}\end{array}\end{array}\right\}\end{array}$ $\delta =4;\omega =6;g=0$ 4 ${\mathbb{T}}_{1}.{\mathbb{T}}_{1}.{\mathbb{T}}_{1}$ $\begin{array}{l}\left\{\begin{array}{cc}1& \begin{array}{cc}23& \begin{array}{cc}114& \begin{array}{cc}23& 1\end{array}\end{array}\end{array}\end{array}\right\}\\ \oplus \left\{\begin{array}{cc}\left(\begin{array}{c}n+2\\ n-1\end{array}\right)& \begin{array}{cc}\left(\begin{array}{c}n+1\\ n-2\end{array}\right)& \begin{array}{cc}\left(\begin{array}{c}n\\ n-3\end{array}\right)& \begin{array}{cc}\left(\begin{array}{c}n-1\\ n-4\end{array}\right)& \left(\begin{array}{c}n-2\\ n-5\end{array}\right)\end{array}\end{array}\end{array}\end{array}\right\}\end{array}$ $\delta =3;\omega =5;g=0$