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 A166443 #17 Jul 27 2024 09:40:54
%S A166443 1,49,2352,112896,5419008,260112384,12485394432,599298932736,
%T A166443 28766348771328,1380784741023744,66277667569139712,
%U A166443 3181328043318705000,152703746079297783552,7329779811806290902168,351829430966701833304320
%N A166443 Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.
%C A166443 The initial terms coincide with those of A170768, although the two sequences are eventually different.
%C A166443 Computed with MAGMA using commands similar to those used to compute A154638.
%H A166443 G. C. Greubel, <a href="/A166443/b166443.txt">Table of n, a(n) for n = 0..500</a>
%H A166443 <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (47,47,47,47,47,47,47,47,47,47,-1128).
%F A166443 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)/(1128*t^11 - 47*t^10 - 47*t^9 - 47*t^8 - 47*t^7 - 47*t^6 - 47*t^5 - 47*t^4 - 47*t^3 - 47*t^2 - 47*t + 1).
%F A166443 From _G. C. Greubel_, Jul 27 2024: (Start)
%F A166443 a(n) = 47*Sum_{j=1..10} a(n-j) - 1128*a(n-11).
%F A166443 G.f.: (1+x)*(1-x^11)/(1 - 48*x + 1175*x^11 - 1128*x^12). (End)
%t A166443 With[{num=Total[2t^Range[10]]+t^11+1,den=Total[-47 t^Range[10]]+ 1128t^11+ 1}, CoefficientList[Series[num/den,{t,0,20}],t]] (* _Harvey P. Dale_, Aug 29 2011 *)
%t A166443 With[{p=1128, q=47}, 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 14 2016; Jul 27 2024 *)
%t A166443 coxG[{11, 1128, -47, 30}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, Jul 27 2024 *)
%o A166443 (Magma)
%o A166443 R<x>:=PowerSeriesRing(Integers(), 30);
%o A166443 f:= func< p,q,x | (1+x)*(1-x^11)/(1-(q+1)*x+(p+q)*x^11-p*x^12) >;
%o A166443 Coefficients(R!( f(1128,47,x) )); // _G. C. Greubel_, Jul 27 2024
%o A166443 (SageMath)
%o A166443 def f(p,q,x): return (1+x)*(1-x^11)/(1-(q+1)*x+(p+q)*x^11-p*x^12)
%o A166443 def A166443_list(prec):
%o A166443 P.<x> = PowerSeriesRing(ZZ, prec)
%o A166443 return P( f(1128,47,x) ).list()
%o A166443 A166443_list(30) # _G. C. Greubel_, Jul 27 2024
%Y A166443 Cf. A154638, A169452, A170768.
%K A166443 nonn
%O A166443 0,2
%A A166443 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009