cp's OEIS Frontend

A170015 Number of reduced words of length n in Coxeter group on 6 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.

%I A170015 #10 May 16 2025 18:44:01
%S A170015 1,6,30,150,750,3750,18750,93750,468750,2343750,11718750,58593750,
%T A170015 292968750,1464843750,7324218750,36621093750,183105468750,
%U A170015 915527343750,4577636718750,22888183593750,114440917968750,572204589843750
%N A170015 Number of reduced words of length n in Coxeter group on 6 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.
%C A170015 The initial terms coincide with those of A003948, although the two sequences are eventually different.
%C A170015 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170015 <a href="/index/Rec#order_36">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, -10).
%F A170015 G.f. (t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 +
%F A170015 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 +
%F A170015 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 +
%F A170015 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4
%F A170015 + 2*t^3 + 2*t^2 + 2*t + 1)/(10*t^36 - 4*t^35 - 4*t^34 - 4*t^33 - 4*t^32
%F A170015 - 4*t^31 - 4*t^30 - 4*t^29 - 4*t^28 - 4*t^27 - 4*t^26 - 4*t^25 - 4*t^24
%F A170015 - 4*t^23 - 4*t^22 - 4*t^21 - 4*t^20 - 4*t^19 - 4*t^18 - 4*t^17 - 4*t^16
%F A170015 - 4*t^15 - 4*t^14 - 4*t^13 - 4*t^12 - 4*t^11 - 4*t^10 - 4*t^9 - 4*t^8 -
%F A170015 4*t^7 - 4*t^6 - 4*t^5 - 4*t^4 - 4*t^3 - 4*t^2 - 4*t + 1)
%t A170015 With[{num=Total[2t^Range[35]]+t^36+1,den=Total[-4 t^Range[35]]+10t^36+ 1},CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Jun 17 2013 *)
%t A170015 coxG[{36,10,-4,30}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, May 16 2025 *)
%K A170015 nonn
%O A170015 0,2
%A A170015 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009