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A166428 Number of reduced words of length n in Coxeter group on 34 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.

%I A166428 #13 Jul 25 2024 21:00:05
%S A166428 1,34,1122,37026,1221858,40321314,1330603362,43909910946,
%T A166428 1449027061218,47817893020194,1577990469666402,52073685498990705,
%U A166428 1718431621466674752,56708243508399656448,1871372035777168520640,61755277180645896490368
%N A166428 Number of reduced words of length n in Coxeter group on 34 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.
%C A166428 The initial terms coincide with those of A170753, although the two sequences are eventually different.
%C A166428 Computed with MAGMA using commands similar to those used to compute A154638.
%H A166428 G. C. Greubel, <a href="/A166428/b166428.txt">Table of n, a(n) for n = 0..500</a>
%H A166428 <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (32,32,32,32,32,32,32,32,32,32,-528).
%F A166428 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)/(528*t^11 - 32*t^10 - 32*t^9 - 32*t^8 - 32*t^7 - 32*t^6 - 32*t^5 - 32*t^4 - 32*t^3 - 32*t^2 - 32*t + 1).
%F A166428 From _G. C. Greubel_, Jul 25 2024: (Start)
%F A166428 a(n) = 32*Sum_{j=1..10} a(n-j) - 528*a(n-11).
%F A166428 G.f.: (1+x)*(1-x^11)/(1 - 33*x + 560*x^11 - 528*x^12). (End)
%t A166428 With[{p=528, q=32}, 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 A166428 coxG[{11, 528, -32, 30}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, Jul 25 2024 *)
%o A166428 (Magma)
%o A166428 R<x>:=PowerSeriesRing(Integers(), 30);
%o A166428 Coefficients(R!( (1+x)*(1-x^11)/(1-33*x+560*x^11-528*x^12) )); // _G. C. Greubel_, Jul 25 2024
%o A166428 (SageMath)
%o A166428 def A166428_list(prec):
%o A166428     P.<x> = PowerSeriesRing(ZZ, prec)
%o A166428     return P( (1+x)*(1-x^11)/(1-33*x+560*x^11-528*x^12) ).list()
%o A166428 A166428_list(30) # _G. C. Greubel_, Jul 25 2024
%Y A166428 Cf. A154638, A169452, A170753.
%K A166428 nonn
%O A166428 0,2
%A A166428 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009