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A226454 The number of squares added in the n-th step of a Pythagoras tree of the 30-60-90 triangle. 3
1, 2, 4, 8, 16, 30, 54, 98, 180, 332, 612, 1120, 2046, 3736 (list; graph; refs; listen; history; text; internal format)



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.


Table of n, a(n) for n=1..14.

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


Cf. A053599.

Sequence in context: A248846 A046127 A271480 * A075529 A005305 A298402

Adjacent sequences:  A226451 A226452 A226453 * A226455 A226456 A226457




Kival Ngaokrajang, Jun 07 2013



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Last modified May 10 05:00 EDT 2021. Contains 343748 sequences. (Running on oeis4.)