This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A166427 #16 Jul 25 2024 15:36:51
%S A166427 1,33,1056,33792,1081344,34603008,1107296256,35433480192,
%T A166427 1133871366144,36283883716608,1161084278931456,37154696925806064,
%U A166427 1188950301625777152,38046409652024328720,1217485108864761234432,38959523483671806394368
%N A166427 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 A166427 The initial terms coincide with those of A170752, although the two sequences are eventually different.
%C A166427 Computed with MAGMA using commands similar to those used to compute A154638.
%H A166427 G. C. Greubel, <a href="/A166427/b166427.txt">Table of n, a(n) for n = 0..500</a>
%H A166427 <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 A166427 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).
%F A166427 From _G. C. Greubel_, Jul 25 2024: (Start)
%F A166427 a(n) = 31*Sum_{j=1..10} a(n-j) - 496*a(n-11).
%F A166427 G.f.: (1+x)*(1-x^11)/(1 - 22*x + 527*x^11 - 496*x^12). (End)
%t A166427 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 A166427 With[{p=496, q=31}, CoefficientList[Series[(1+t)*(1-t^11)/(1-(q+1)*t + (p+q)*t^11-p*t^12), {t,0,40}], t]] (* _G. C. Greubel_, May 13 2016; Jul 25 2024 *)
%t A166427 coxG[{11, 496, -31, 30}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, Jul 25 2024 *)
%o A166427 (Magma)
%o A166427 R<x>:=PowerSeriesRing(Integers(), 30);
%o A166427 Coefficients(R!( (1+x)*(1-x^11)/(1-32*x+527*x^11-496*x^12) )); // _G. C. Greubel_, Jul 25 2024
%o A166427 (SageMath)
%o A166427 def A166427_list(prec):
%o A166427 P.<x> = PowerSeriesRing(ZZ, prec)
%o A166427 return P( (1+x)*(1-x^11)/(1-32*x+527*x^11-496*x^12) ).list()
%o A166427 A166427_list(30) # _G. C. Greubel_, Jul 25 2024
%Y A166427 Cf. A154638, A169452, A170752.
%K A166427 nonn
%O A166427 0,2
%A A166427 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009