Here is the table:
$\begin{array}{c} 0\\ 1\\ 1& 1\\ 3& 2& 3\\ 5& 3& 3& 5\\ 11 &8 &10 &8 &11\\ 21 &13 &14 &14 &13 &21\\ 43 &30 &37 &36 &37 &30 &43\\ 85 &55 &61 &55 &55 &61 &55 &85\\ 171 &116 &140 &140 &146 &140 &140 &116 &171 \end{array}$
In this triangle like table, I am unable to find the relation between columnwise. Say for 1st column, I have found the relation $A(n)= A(n-1)+2A(n-2)$.
For the 2nd column, I have the relation $A(n)= A(n-1)+2A(n-2) + x$ [ where $x$ is $-1$ for even row number and $+1$ for odd].
But for other columns, I have not found the relations yet. Can anyone help me find a generalized equation to generate the table?