References to A154638

a(n) is the number of unique reduced words of length n (i.e. all possible length-reducing cancellations have been applied and words that are equal are counted only once) in the Coxeter group of "Apollonian reflections" in three dimensions. This group has five generators, satisfying (S_i)^2 = (S_i S_j)^3 = I.
1, 5, 20, 70, 240, 810, 2730, 9180, 30870, 103770, 348840, 1172610, 3941730

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