Mutually Visible Point Pairs in a Three-Row Hexagonal Lattice Configuration

We consider lattice point configurations with rows of 2n+1, 4n+1 and 2n+1 points (3-5-3, 5-9-5, 7-13-7, ...). Two points are mutually visible if no other point of the configuration lies on the segment joining them. We prove by direct counting that the number of mutually visible pairs is 18n^2 + 22n + 2. We also report an observed formula for the product of the three central-column degrees (checked by computer for n = 1..30, not proven). The text was prepared with the assistance of an AI model (Claude, Anthropic); the formula was also verified by computer.