**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*

*1 seqfan posts*

Index of A-numbers in seqfan: by ascending order by month by frequency by keyword

Links to OEIS content are included according to The OEIS End-User License Agreement .