cp's OEIS Frontend

A170088 Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.

%I A170088 #9 Nov 26 2016 10:06:02
%S A170088 1,31,930,27900,837000,25110000,753300000,22599000000,677970000000,
%T A170088 20339100000000,610173000000000,18305190000000000,549155700000000000,
%U A170088 16474671000000000000,494240130000000000000,14827203900000000000000
%N A170088 Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.
%C A170088 The initial terms coincide with those of A170750, although the two sequences are eventually different.
%C A170088 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170088 <a href="/index/Rec#order_37">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, 29, -435).
%F A170088 G.f. (t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 +
%F A170088 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 +
%F A170088 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 +
%F A170088 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 +
%F A170088 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(435*t^37 - 29*t^36 - 29*t^35 -
%F A170088 29*t^34 - 29*t^33 - 29*t^32 - 29*t^31 - 29*t^30 - 29*t^29 - 29*t^28 -
%F A170088 29*t^27 - 29*t^26 - 29*t^25 - 29*t^24 - 29*t^23 - 29*t^22 - 29*t^21 -
%F A170088 29*t^20 - 29*t^19 - 29*t^18 - 29*t^17 - 29*t^16 - 29*t^15 - 29*t^14 -
%F A170088 29*t^13 - 29*t^12 - 29*t^11 - 29*t^10 - 29*t^9 - 29*t^8 - 29*t^7 -
%F A170088 29*t^6 - 29*t^5 - 29*t^4 - 29*t^3 - 29*t^2 - 29*t + 1)
%t A170088 With[{num=Total[2t^Range[36]]+t^37+1,den=Total[-29 t^Range[36]]+ 435t^37+ 1},CoefficientList[Series[num/den,{t,0,20}],t]] (* _Harvey P. Dale_, Dec 08 2011 *)
%K A170088 nonn
%O A170088 0,2
%A A170088 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009