To Math Fun, Seq Fan: I ran into my distinguished (former) colleague Colin Mallows yesterday, and he said that it would be nice if someone would extend his sequence A154638. Take the infinite reflection group with 5 generators S_1, ..., S_5, satisfying (S_i)^2 = (S_i S_j)^3 = I, and let a(n) be number of distinct elements whose minimal representation as a product of generators has length n: 1, 5, 20, 70, 240, 780, 2730, .. (for n>= 0) Can anybody help extend this sequence? Is there a generating function? What about other groups? This might be a gaping hole in the OEIS! There must be a huge literature on this problem. The books that I know about that might be related, Lyndom & Schupp, Combinatorial Group Theory, Magnus, Karrass, Solitar, same title, Johnson, Presentations of Groups, aren't exactly full of sequences, as far as I can tell. Can some expert please help? Neil