cp's OEIS Frontend

A170040 Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.

%I A170040 #8 Nov 26 2016 09:45:36
%S A170040 1,31,930,27900,837000,25110000,753300000,22599000000,677970000000,
%T A170040 20339100000000,610173000000000,18305190000000000,549155700000000000,
%U A170040 16474671000000000000,494240130000000000000,14827203900000000000000
%N A170040 Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.
%C A170040 The initial terms coincide with those of A170750, although the two sequences are eventually different.
%C A170040 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170040 <a href="/index/Rec#order_36">Index entries for linear recurrences with constant coefficients</a>, signature (29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, -435).
%F A170040 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 A170040 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 A170040 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 A170040 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 A170040 + 2*t^3 + 2*t^2 + 2*t + 1)/(435*t^36 - 29*t^35 - 29*t^34 - 29*t^33 -
%F A170040 29*t^32 - 29*t^31 - 29*t^30 - 29*t^29 - 29*t^28 - 29*t^27 - 29*t^26 -
%F A170040 29*t^25 - 29*t^24 - 29*t^23 - 29*t^22 - 29*t^21 - 29*t^20 - 29*t^19 -
%F A170040 29*t^18 - 29*t^17 - 29*t^16 - 29*t^15 - 29*t^14 - 29*t^13 - 29*t^12 -
%F A170040 29*t^11 - 29*t^10 - 29*t^9 - 29*t^8 - 29*t^7 - 29*t^6 - 29*t^5 - 29*t^4
%F A170040 - 29*t^3 - 29*t^2 - 29*t + 1)
%t A170040 With[{num=Total[2t^Range[35]]+t^36+1,den=Total[-29 t^Range[35]]+435t^36+ 1},CoefficientList[Series[num/den,{t,0,20}],t]] (* _Harvey P. Dale_, Nov 29 2013 *)
%K A170040 nonn
%O A170040 0,2
%A A170040 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009