Let $A=\left[\begin{array}{ccc}1& 0& 0\\ 1& 1& 0\\ 1& 1& 1\end{array}\right] and B=A^{20}$. Then the sum of the elements of the first column of B

$A^2=\left[\begin{array}{ccc}1& 0& 0\\ 1& 1& 0\\ 1& 1& 0\end{array}\right] \left[\begin{array}{ccc}1& 0& 0\\ 1& 1& 0\\ 1& 1& 1\end{array}\right]=\left[\begin{array}{ccc}1& 0& 0\\ 2& 1& 0\\ 3& 2& 1\end{array}\right], A^3=\left[\begin{array}{ccc}1& 0& 0\\ 1& 1& 0\\ 1& 1& 1\end{array}\right] \left[\begin{array}{ccc}1& 0& 0\\ 2& 1& 0\\ 3& 2& 1\end{array}\right]=\left[\begin{array}{ccc}1& 0& 0\\ 3& 1& 0\\ 6& 3& 1\end{array}\right]$

$A^4=\left[\begin{array}{ccc}1& 0& 0\\ 1& 1& 0\\ 1& 0& 1\end{array}\right] \left[\begin{array}{ccc}1& 0& 0\\ 3& 1& 0\\ 6& 3& 1\end{array}\right]=\left[\begin{array}{ccc}1& 0& 0\\ 4& 1& 0\\ 10& 4& 1\end{array}\right] . . . . . A^{20}=\left[\begin{array}{ccc}1& 0& 0\\ 20& 1& 0\\ 210& 20& 1\end{array}\right]$

Sum of the elements of first column of $A^{20}$ is 1 + 20 + 210 = 231.