Find Out How Many Combinations of n Squares Exist

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In the picture attached I have tried to list the different shapes you can get when you attach, 1, 2, 3, 4 squares, but, as you can imagine, when n gets bigger the number of combinations gets incredibly large. Is there are way to see how many possible configurations there is for n squares, and the different perimeters of these shapes?
If not is it possible for equilateral triangles?

 

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In the picture attached I have tried to list the different shapes you can get when you attach, 1, 2, 3 squares, but, as you can imagine, when n gets bigger the number of combinations gets incredibly large. Is there are way to see how many possible configurations there is for n squares, and the different perimeters of these shapes?
If not is it possible for equilateral triangles?

Can't see the attachment
EDIT:Now it's there.That is very similar to Isomers of hydrocarbons(Chemistry)

 

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now :)