cp's OEIS Frontend

A170111 Number of reduced words of length n in Coxeter group on 6 generators S_i with relations (S_i)^2 = (S_i S_j)^38 = I.

%I A170111 #8 Apr 18 2020 15:17:59
%S A170111 1,6,30,150,750,3750,18750,93750,468750,2343750,11718750,58593750,
%T A170111 292968750,1464843750,7324218750,36621093750,183105468750,
%U A170111 915527343750,4577636718750,22888183593750,114440917968750,572204589843750
%N A170111 Number of reduced words of length n in Coxeter group on 6 generators S_i with relations (S_i)^2 = (S_i S_j)^38 = I.
%C A170111 The initial terms coincide with those of A003948, although the two sequences are eventually different.
%C A170111 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170111 <a href="/index/Rec#order_38">Index entries for linear recurrences with constant coefficients</a>, signature (4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, -10).
%F A170111 G.f. (t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 +
%F A170111 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 +
%F A170111 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 +
%F A170111 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 +
%F A170111 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(10*t^38 - 4*t^37 -
%F A170111 4*t^36 - 4*t^35 - 4*t^34 - 4*t^33 - 4*t^32 - 4*t^31 - 4*t^30 - 4*t^29 -
%F A170111 4*t^28 - 4*t^27 - 4*t^26 - 4*t^25 - 4*t^24 - 4*t^23 - 4*t^22 - 4*t^21 -
%F A170111 4*t^20 - 4*t^19 - 4*t^18 - 4*t^17 - 4*t^16 - 4*t^15 - 4*t^14 - 4*t^13 -
%F A170111 4*t^12 - 4*t^11 - 4*t^10 - 4*t^9 - 4*t^8 - 4*t^7 - 4*t^6 - 4*t^5 - 4*t^4
%F A170111 - 4*t^3 - 4*t^2 - 4*t + 1)
%t A170111 coxG[{38,10,-4,30}] (* The coxG program is at A169452 *)  (* _Harvey P. Dale_, Apr 18 2020 *)
%K A170111 nonn
%O A170111 0,2
%A A170111 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009