OFFSET
1,2
COMMENTS
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.
LINKS
Kival Ngaokrajang, Pythagoras tree by isosceles right triangle for n = 1..12
Kival Ngaokrajang, Pythagoras tree by 30-60-90 triangle for n = 1..11
Wikipedia, Pythagoras tree
CROSSREFS
KEYWORD
nonn
AUTHOR
Kival Ngaokrajang, Jun 07 2013
STATUS
approved