I was playing around with these magnetic balls, making hexagons. These photos show the "hex numbers" H_1, H_2, H_4, and H_16. You can see that H_n=6T_{n-1}+1, where T_k is the kth "triangular number." The formula for hex numbers is H_k=3k^2-3k+1. So, the large hex has 721 balls.
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@divbyzero in case you haven't tried it, my absolute favorite thing to do with these is building a "wrinkly" regular n-gon where you start with a ring of like 7 - 15 balls depending on the desired level of wrinkliness. it's a bit tricky to get the requisite 2 balls per ball on the second loop, but more or less the same as making a hexagon afterwards
