How many Happy triangles?

Level pending

How many distinct equilateral triangles can we count in the diagram below such that

  1. every vertex of the triangle is a vertex on the diagram, and
  2. the triangle is oriented in the same direction as triangle \(ABC?\)


Bonus and Details:

  • What's the general formula for the corresponding question with the diagram having \(n\) rows in the triangular grid?
  • This is not an original question from me.
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