the group is , and the picture:
Correctly predicts the next one. It is A164001 in the OEIS data-base. Dubbed “Spiral of triangles around a hexagon“. It has the generating function , Why would it be? :) . This another is A000931.
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Filed under free group, math, sum of reciprocals
Tagged as A000931, A164001, free product, OEIS, OEIS A164001, sum of reciprocals