TITLE: In how many different ways can a 9-panel comic grid be used?
QUESTION [61 upvotes]: While writing my answer to Why does “Watchmen” use the 9-panel grid? I used this picture to indicate the many ways it can be divided into groups (which may be used for the panels of a comic, as was the case in “Watchmen”):

 Image source 
Afterwards, it has been pointed out to me in a comment that there are some combinations that are not present in this picture:

The $81$ variations on the $9$ panel grid in that diagram don't exhaust the possibilities -- there are certainly many others. For example, this one is one of the many that aren't shown there.


Another comment says that the 9-panel grid can be used in $4096$ different ways:

The are $12$ interior borders, each of which can be included or excluded in a particular layout. That's $2^{12} = 4096$ possibilities.
A two-page spread treats two $3 \times 3$ grids as a single $6 \times 3$ grid with $21$ internal borders, for $2,097,152$ possibilities.

How can I calculate that? I tried the following:

There a $3$ ways to group the third row.
That leaves us with $4$ panels in 2nd and 3rd rows. I count $4$ ways to group those.
The $12$ combinations so far must be multiplied by $4$ (because I can rotate them) and by $2$ (because I can mirror them).

This gives me $96$ variations. The picture above has $81$; the comment said there are $4096$.
Is there a layman-friendly geometrical solution? I'm not really interested in a precise value (a lot is enough for me), I'm more interested in the technique or a rule. Is there a general rule for a n-by-n grid?
To clarify: panels must be rectangular, i.e. they must be formed by merging some of the $9$ panels horizontally or vertically:

REPLY [6 votes]: While this is a fascinating discussion, the reality is that many of these grids would be unreadable because it's not immediately apparent which panel comes next is a sequence. A vertical panel on the right, with stacks on the left is problematic because the reader doesn't know whether to read to the right or down. Of those shown above, only $175$ of them are functional.