%I #17 Dec 03 2025 17:11:31

%S 1,30,870,25230,731670,21218430,615334470,17844699630,517496289270,

%T 15007392388830,435214379276070,12621216999005595,366015292971149640,

%U 10614443496162974160,307818861388715654040,8926746980272446665760

%N Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.

%C The initial terms coincide with those of A170749, although the two sequences are eventually different.

%C Computed with Magma using commands similar to those used to compute A154638.

%H G. C. Greubel, <a href="/A166424/b166424.txt">Table of n, a(n) for n = 0..500</a>

%H <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (28,28,28,28,28,28,28,28,28,28,-406).

%F 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)/(406*t^11 - 28*t^10 - 28*t^9 - 28*t^8 - 28*t^7 - 28*t^6 - 28*t^5 - 28*t^4 - 28*t^3 - 28*t^2 - 28*t + 1).

%F From _G. C. Greubel_, Jul 25 2024: (Start)

%F a(n) = 28*Sum_{j=1..10} a(n-j) - 406*a(n-11).

%F G.f.: (1+x)*(1-x^11)/(1 - 29*x + 434*x^11 - 406*x^12). (End)

%t With[{p=406, q=28}, 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 coxG[{11,406,-28}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Oct 12 2016 *)

%o (Magma)

%o R<x>:=PowerSeriesRing(Integers(), 30);

%o Coefficients(R!( (1+x)*(1-x^11)/(1-29*x+434*x^11-406*x^12) )); // _G. C. Greubel_, Jul 25 2024

%o (SageMath)

%o def A166424_list(prec):

%o P.<x> = PowerSeriesRing(ZZ, prec)

%o return P( (1+x)*(1-x^11)/(1-29*x+434*x^11-406*x^12) ).list()

%o A166424_list(30) # _G. C. Greubel_, Jul 25 2024

%Y Cf. A154638, A169452, A170749.

%K nonn

%O 0,2

%A _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009