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A166411 Number of reduced words of length n in Coxeter group on 17 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.

%I A166411 #19 Jul 23 2024 18:55:59
%S A166411 1,17,272,4352,69632,1114112,17825792,285212672,4563402752,
%T A166411 73014444032,1168231104512,18691697672056,299067162750720,
%U A166411 4785074603976840,76561193663074560,1224979098600314880,19599665577462988800
%N A166411 Number of reduced words of length n in Coxeter group on 17 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.
%C A166411 The initial terms coincide with those of A170736, although the two sequences are eventually different.
%C A166411 Computed with MAGMA using commands similar to those used to compute A154638.
%H A166411 G. C. Greubel, <a href="/A166411/b166411.txt">Table of n, a(n) for n = 0..500</a>
%H A166411 <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (15,15,15,15,15,15,15,15,15,15,-120).
%F A166411 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)/(120*t^11 - 15*t^10 - 15*t^9 - 15*t^8 - 15*t^7 - 15*t^6 - 15*t^5 - 15*t^4 - 15*t^3 - 15*t^2 - 15*t + 1).
%F A166411 From _G. C. Greubel_, Jul 23 2024: (Start)
%F A166411 a(n) = 15*Sum_{j=1..10} a(n-j) - 120*a(n-11).
%F A166411 G.f.: (1+x)*(1-x^11)/(1 - 16*x + 135*x^11 - 120*x^12). (End)
%t A166411 With[{p=120, q=15}, 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 12 2016; Jul 23 2024 *)
%t A166411 coxG[{11,120,-15}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Sep 29 2016 *)
%o A166411 (Magma)
%o A166411 R<x>:=PowerSeriesRing(Integers(), 30);
%o A166411 Coefficients(R!( (1+x)*(1-x^11)/(1-16*x+135*x^11-120*x^12) )); // _G. C. Greubel_, Jul 23 2024
%o A166411 (SageMath)
%o A166411 def A166411_list(prec):
%o A166411     P.<x> = PowerSeriesRing(ZZ, prec)
%o A166411     return P( (1+x)*(1-x^11)/(1-16*x+135*x^11-120*x^12) ).list()
%o A166411 A166411_list(30) # _G. C. Greubel_, Jul 23 2024
%Y A166411 Cf. A154638, A169452, A170736.
%K A166411 nonn
%O A166411 0,2
%A A166411 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009