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There are lots of patterns hidden away in the triangle, enough to fill a reasonably sized book. Here are just a few of the most obvious ones:

  1. The entries on the border of the triangle are all 1.

  2. Any entry not on the border is the sum of the two entries above it.

  3. The triangle is symmetric. In any row, entries on the left side are mirrored on the right side.

  4. The sum of all entries on a given row is a power of 2. (You should check this!)

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