Your task: given an integer
n, generate an embedded hexagon pattern following the below rules, to the nth depth.
An embedded hexagon has the basic shape of this: (
__ / \ \__/
____ / \ \ /\__/ \ \ / \____/ ________ / \ \ \ /\__/ \ \ /\ / \ / \____/ \ \ / \ / \ / \________/
The length of each side is 2 times the length of the same side in the previous depth times two. The top and bottom sides are 2 characters long when
n=0 and the rest start out as 1 character long. The non top-bottom side lengths should be
2^n long (OEIS: A000079) and the top and bottom sides should follow the rule
2^(n+1) (same OEIS).
The current hexagons are 0-indexed, you may chose to use 1-indexed if you want.
This is code-golf, so the shortest answer wins!