|
%I #13 Nov 24 2016 09:28:05
%S 1,33,1056,33792,1081344,34603008,1107296256,35433480192,
%T 1133871366144,36283883716608,1161084278931456,37154696925806064,
%U 1188950301625777152,38046409652024328720,1217485108864761234432,38959523483671806394368
%N Number of reduced words of length n in Coxeter group on 33 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.
%C The initial terms coincide with those of A170752, although the two sequences are eventually different.
%C Computed with MAGMA using commands similar to those used to compute A154638.
%H G. C. Greubel, <a href="/A166427/b166427.txt">Table of n, a(n) for n = 0..500</a>
%H <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (31, 31, 31, 31, 31, 31, 31, 31, 31, 31, -496).
%F G.f.: (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 + 2*t^2 + 2*t + 1)/(496*t^11 - 31*t^10 - 31*t^9 - 31*t^8 - 31*t^7 - 31*t^6 - 31*t^5 - 31*t^4 - 31*t^3 - 31*t^2 - 31*t + 1).
%t With[{num=Total[2t^Range[10]]+t^11+1,den=Total[-31 t^Range[10]]+496t^11+ 1}, CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Aug 16 2011 *)
%t CoefficientList[Series[(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 + 2*t^2 + 2*t + 1)/(496*t^11 - 31*t^10 - 31*t^9 - 31*t^8 - 31*t^7 - 31*t^6 - 31*t^5 - 31*t^4 - 31*t^3 - 31*t^2 - 31*t + 1 ), {t, 0, 50}], t] (* _G. C. Greubel_, May 13 2016 *)
%K nonn
%O 0,2
%A _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009
|
