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A166422 Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.

%I A166422 #16 Jul 25 2024 14:48:38
%S A166422 1,28,756,20412,551124,14880348,401769396,10847773692,292889889684,
%T A166422 7908027021468,213516729579636,5764951698649794,155653695863534232,
%U A166422 4202649788315149080,113471544284501595192,3063731695681342461048
%N A166422 Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.
%C A166422 The initial terms coincide with those of A170747, although the two sequences are eventually different.
%C A166422 Computed with MAGMA using commands similar to those used to compute A154638.
%H A166422 G. C. Greubel, <a href="/A166422/b166422.txt">Table of n, a(n) for n = 0..500</a>
%H A166422 <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (26,26,26,26,26,26,26,26,26,26,-351).
%F A166422 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)/(351*t^11 - 26*t^10 - 26*t^9 - 26*t^8 - 26*t^7 - 26*t^6 - 26*t^5 - 26*t^4 - 26*t^3 - 26*t^2 - 26*t + 1).
%F A166422 From _G. C. Greubel_, Jul 25 2024: (Start)
%F A166422 a(n) = 26*Sum_{j=1..10} a(n-j) - 351*a(n-11).
%F A166422 G.f.: (1+x)*(1-x^11)/(1 - 27*x + 377*x^11 - 351*x^12). (End)
%t A166422 With[{p=351, q=26}, 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 A166422 coxG[{11,351,-26}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Dec 22 2019 *)
%o A166422 (Magma)
%o A166422 R<x>:=PowerSeriesRing(Integers(), 30);
%o A166422 Coefficients(R!( (1+x)*(1-x^11)/(1-27*x+377*x^11-351*x^12) )); // _G. C. Greubel_, Jul 25 2024
%o A166422 (SageMath)
%o A166422 def A166422_list(prec):
%o A166422     P.<x> = PowerSeriesRing(ZZ, prec)
%o A166422     return P( (1+x)*(1-x^11)/(1-27*x+377*x^11-351*x^12) ).list()
%o A166422 A166422_list(30) # _G. C. Greubel_, Jul 25 2024
%Y A166422 Cf. A154638, A169452, A170747.
%K A166422 nonn
%O A166422 0,2
%A A166422 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009