cp's OEIS Frontend

A169526 Number of reduced words of length n in Coxeter group on 33 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.

%I A169526 #8 Nov 26 2016 07:38:50
%S A169526 1,33,1056,33792,1081344,34603008,1107296256,35433480192,
%T A169526 1133871366144,36283883716608,1161084278931456,37154696925806592,
%U A169526 1188950301625810944,38046409652025950208,1217485108864830406656,38959523483674573012992
%N A169526 Number of reduced words of length n in Coxeter group on 33 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.
%C A169526 The initial terms coincide with those of A170752, although the two sequences are eventually different.
%C A169526 Computed with MAGMA using commands similar to those used to compute A154638.
%H A169526 <a href="/index/Rec#order_34">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, -496).
%F A169526 G.f. (t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 +
%F A169526 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 +
%F A169526 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 +
%F A169526 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 +
%F A169526 2*t + 1)/(496*t^34 - 31*t^33 - 31*t^32 - 31*t^31 - 31*t^30 - 31*t^29 -
%F A169526 31*t^28 - 31*t^27 - 31*t^26 - 31*t^25 - 31*t^24 - 31*t^23 - 31*t^22 -
%F A169526 31*t^21 - 31*t^20 - 31*t^19 - 31*t^18 - 31*t^17 - 31*t^16 - 31*t^15 -
%F A169526 31*t^14 - 31*t^13 - 31*t^12 - 31*t^11 - 31*t^10 - 31*t^9 - 31*t^8 -
%F A169526 31*t^7 - 31*t^6 - 31*t^5 - 31*t^4 - 31*t^3 - 31*t^2 - 31*t + 1)
%t A169526 With[{num=Total[2t^Range[33]]+t^34+1,den=Total[-31 t^Range[33]]+496t^34+ 1},CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Mar 06 2013 *)
%K A169526 nonn
%O A169526 0,2
%A A169526 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009