A226454 The number of squares added in the n-th step of a Pythagoras tree of the 30-60-90 triangle.

1, 2, 4, 8, 16, 30, 54, 98, 180, 332, 612, 1120, 2046, 3736

Offset: 1

Author

Kival Ngaokrajang, Jun 07 2013

Keywords

• nonn

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

Cf. A053599.