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A166382 Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.

%I A166382 #21 Jul 23 2024 15:04:46
%S A166382 1,15,210,2940,41160,576240,8067360,112943040,1581202560,22136835840,
%T A166382 309915701760,4338819824535,60743477542020,850408685567805,
%U A166382 11905721597662620,166680102363263580,2333521433029506720
%N A166382 Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.
%C A166382 The initial terms coincide with those of A170734, although the two sequences are eventually different.
%C A166382 Computed with MAGMA using commands similar to those used to compute A154638.
%H A166382 G. C. Greubel, <a href="/A166382/b166382.txt">Table of n, a(n) for n = 0..500</a>
%H A166382 <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (13,13,13,13,13,13,13,13,13,13,-91).
%F A166382 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)/(91*t^11 - 13*t^10 - 13*t^9 - 13*t^8 - 13*t^7 - 13*t^6 - 13*t^5 - 13*t^4 - 13*t^3 - 13*t^2 - 13*t + 1).
%F A166382 From _G. C. Greubel_, Jul 23 2024: (Start)
%F A166382 a(n) = 13*Sum_{j=1..10} a(n-j) - 91*a(n-11).
%F A166382 G.f.: (1+x)*(1 - x^11)/(1 - 14*x + 104*x^11 - 91*x^12). (End)
%t A166382 With[{a=91, b=13}, CoefficientList[Series[(1+t)*(1-t^11)/(1-(b+1)*t +(a+b)*t^11-a*t^12), {t,0,40}], t]] (* _G. C. Greubel_, May 10 2016; Jul 23 2024 *)
%t A166382 coxG[{11,91,-13}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jan 25 2019 *)
%o A166382 (Magma)
%o A166382 R<x>:=PowerSeriesRing(Integers(), 30);
%o A166382 Coefficients(R!( (1+x)*(1-x^11)/(1-14*x+104*x^11-91*x^12) )); // _G. C. Greubel_, Jul 23 2024
%o A166382 (SageMath)
%o A166382 def A166382_list(prec):
%o A166382     P.<x> = PowerSeriesRing(ZZ, prec)
%o A166382     return P( (1+x)*(1-x^11)/(1-14*x+104*x^11-91*x^12) ).list()
%o A166382 A166382_list(30) # _G. C. Greubel_, Jul 23 2024
%Y A166382 Cf. A154638, A169452, A170734.
%K A166382 nonn
%O A166382 0,2
%A A166382 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009