Identifying an equation for calculating nth iteration of square growth

Hi,

Apologies if i have posted this question in the wrong forum , but I am a newbie

My colleages and I have been trying to solve a 12 year old homework question which has us baffled (maybe irrational)

The question regards how to express the nth iteration of a square growth programme - I thought this might be Koch equation :-(

Anyway , here goes

The square can only be added if the adjacent face of an existing square is free and new square will not touch any other square.

The sequence of adding squares therefore follows

Step 0 = 1 Square

Step 1 = 4 Squares

Step 2 = 4 Squares

Step 3 = 12 Squares

Step 4 = 4 Squares

Step 5 = 12 Squares

Step 6 = 12 Squares

Step 7 = 36 Squares

Any thoughts or idea would be much appreciated :-)