Puzzle: $$\begin{array}{}\boxed{3\;\,}&\boxed{150\;\;\;\,}&\boxed{12\;\;\;\,}\\\boxed{7\;\,}&\boxed{3164\;\,}&\boxed{56\;\;\;\,}\\\boxed{16}&\boxed{74112}&\boxed{272\;\;}\\\boxed{32}&\boxed{\text{?}\;\;\;\;\;\;\,}&\boxed{1024\,}\end{array}$$
We have to figure out the question mark.
My effort:
I have tried almost for half-an-hour, but can't seem to work out the rule being followed here. I tried
$$\begin{align}
7 - 3 &= 2^2\\
16 - 7 &= 3^2\\
32 - 16 &= 4^2
\end{align}$$
This was the only sequence I could figure out but it only works for the first column.
I need help figuring this out, along with a suitable explanation of the answer.
Note: This is not a homework question.