Originally posted by Harvey
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I forgot to mention
the third layer does not double as one may mistakenly assume since the third layer doubles the second. But instead, we see a mathematical progression where there are always 6 vertices on the hexagon. Since each side of the hexagon represents an equilateral triangle, we find that the vertices are shared. So the formula for any layer is the six sides of the hexagon, times the quantity of circles for a side, minus six (because of the shared vertices).
For example, on layer 1 we have two circles per side times six sides = 12 minus 6 shared vertices = 6 total circles.
Sides x Circles - vertices = total circles in the layer
Layer 2: 6 x 3 = 18 and 18 - 6 = 12
Layer 3: 6 x 4 = 24 and 24 - 6 = 18
Layer 4: 6 x 5 = 30 and 30 - 6 = 24
Layer 5,000: 6 x 5001 = 30,006 and 30,006 - 6 = 30,000
You may have noticed the other sequence as well. The number of circles for any given side is just one more than the layer.
Sorry to have neglected this before.

EDIT TO ADD:
Pipe is purposely bundled in this configuration because it stacks very nicely hexagonally - too bad the yard hands didn't realize that here
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