# Problem 570: Snowflakes
A snowflake of order n is formed by overlaying an equilateral triangle
(rotated by 180 degrees) onto each equilateral triangle of the same size
in a snowflake of order n-1. A snowflake of order 1 is a single
equilateral triangle. Some areas of the snowflake are overlaid
repeatedly. In the above picture, blue represents the areas that are one
layer thick, red two layers thick, yellow three layers thick, and so on.
For an order n snowflake, let A(n) be the number of triangles that are
one layer thick, and let B(n) be the number of triangles that are three
layers thick. Define G(n) = gcd(A(n), B(n)). E.g. A(3) = 30, B(3) = 6,
G(3)=6 A(11) = 3027630, B(11) = 19862070, G(11) = 30 Further, G(500) =
186 and \$\\sum\_{n=3}\^{500}G(n)=5124\$ Find \$\\displaystyle
\\sum\_{n=3}\^{10\^7}G(n)\$.