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%I #11 Jul 10 2013 03:33:29
%S 1,2,4,8,16,30,56,102,186,340,624,1148
%N The number of squares added in the n-th step of a Pythagoras tree of the 30-60-90 triangle, using the rule larger squares come first.
%C Growth of the Pythagoras tree based on the triangle with internal angles of 30, 60 and 90 degrees.
%C The generating rule is expansion in sequential order on each stage; the larger squares (opposite to the 60 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.
%C The non-overlap rule limits the growth of the sequence to a(n+1) <= 2*a(n).
%C For Pythagoras tree based on isosceles right triangle with the same rule, the sequence will be A053599(n-1) + 1.
%H Kival Ngaokrajang, <a href="/A227298/a227298.jpg">Illustration for n = 1..11</a>
%Y Cf. A053599, A226454.
%K nonn,more
%O 1,2
%A _Kival Ngaokrajang_, Jul 05 2013