Growth of the Pythagoras tree based on the triangle with internal angles of 30, 60 and 90 degrees.
The generating rule is expansion in sequential order on each stage; the smaller squares (opposite to the 30 deg angle) come first. The generating order labeled by "stage-number" starts as 1-1; 2-1, 2-2; 3-1, 3-2, 3-3, 3-4;...and so on. Overlap is prohibited, i.e., if any part of a new element in the next generating order cuts into any previous (existing, lower order) one, that new elements will be not be inserted/added: lower generating orders have precedence over higher generating orders.
The non-overlap rule limits the growth of the sequence to a(n+1) <= 2*a(n).
For Pythagoras tree based on isosceles right triangle with the same rule, the sequence will be A053599(n-1) + 1.