I started playing with a recursive solution that builds grids from smaller grids. Bonus: This method naturally omits permutations.

For example, given 

2x2, 2 syms:

AA  AB  AB
BB  AB  BA

[download]
One can overlap the 2x2 grids to form: 
3x3, 2 syms:

13    22    31    33    33
13    33    31    22    33

AAB   ABA   ABB   ABA   ABA
BBA   ABA   BAA   BAB   BAB
AAB   BAB   ABB   BAB   ABA

[download]

I think it might be possible to turn this into an efficient solution for counting the arrangements instead of generating them.

That's all I had time to do for now.

Update: At time of writing, I thought 

F
FF

[download]
wasn't allowed. The concept still applies, although there would be a lot more possible grids.

In reply to Re^3: Pattern enumeration. by ikegami
in thread Pattern enumeration. by BrowserUk

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