cp's OEIS Frontend

A169574 Number of reduced words of length n in Coxeter group on 33 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.

%I A169574 #8 Nov 26 2016 09:32:25
%S A169574 1,33,1056,33792,1081344,34603008,1107296256,35433480192,
%T A169574 1133871366144,36283883716608,1161084278931456,37154696925806592,
%U A169574 1188950301625810944,38046409652025950208,1217485108864830406656,38959523483674573012992
%N A169574 Number of reduced words of length n in Coxeter group on 33 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.
%C A169574 The initial terms coincide with those of A170752, although the two sequences are eventually different.
%C A169574 Computed with MAGMA using commands similar to those used to compute A154638.
%H A169574 <a href="/index/Rec#order_35">Index entries for linear recurrences with constant coefficients</a>, signature (31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, -496).
%F A169574 G.f. (t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 +
%F A169574 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 +
%F A169574 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 +
%F A169574 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3
%F A169574 + 2*t^2 + 2*t + 1)/(496*t^35 - 31*t^34 - 31*t^33 - 31*t^32 - 31*t^31 -
%F A169574 31*t^30 - 31*t^29 - 31*t^28 - 31*t^27 - 31*t^26 - 31*t^25 - 31*t^24 -
%F A169574 31*t^23 - 31*t^22 - 31*t^21 - 31*t^20 - 31*t^19 - 31*t^18 - 31*t^17 -
%F A169574 31*t^16 - 31*t^15 - 31*t^14 - 31*t^13 - 31*t^12 - 31*t^11 - 31*t^10 -
%F A169574 31*t^9 - 31*t^8 - 31*t^7 - 31*t^6 - 31*t^5 - 31*t^4 - 31*t^3 - 31*t^2 -
%F A169574 31*t + 1)
%t A169574 With[{num=Total[2t^Range[34]]+t^35+1,den=Total[-31 t^Range[34]]+ 496t^35+1},CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Jun 26 2012 *)
%K A169574 nonn
%O A169574 0,2
%A A169574 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009