A166425 - OEIS

%I #16 Jul 25 2024 20:59:38

%S 1,31,930,27900,837000,25110000,753300000,22599000000,677970000000,

%T 20339100000000,610173000000000,18305189999999535,549155699999972100,

%U 16474670999998744965,494240129999949807900,14827203899998118005500

%N Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.

%C The initial terms coincide with those of A170750, 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="/A166425/b166425.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 (29,29,29,29,29,29,29,29,29,29,-435).

%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)/(435*t^11 - 29*t^10 - 29*t^9 - 29*t^8 - 29*t^7 - 29*t^6 - 29*t^5 - 29*t^4 - 29*t^3 - 29*t^2 - 29*t + 1).

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

%F a(n) = 29*Sum_{j=1..10} a(n-j) - 435*a(n-11).

%F G.f.: (1+x)*(1-x^11)/(1 - 30*x + 464*x^11 - 435*x^12). (End)

%t With[{p=435, q=29}, 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[{11,435,-29}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Dec 26 2021 *)

%o (Magma)

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

%o Coefficients(R!( (1+x)*(1-x^11)/(1-30*x+464*x^11-435*x^12) )); // _G. C. Greubel_, Jul 25 2024

%o (SageMath)

%o def A166425_list(prec):

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

%o     return P( (1+x)*(1-x^11)/(1-30*x+464*x^11-435*x^12) ).list()

%o A166425_list(30) # _G. C. Greubel_, Jul 25 2024

%Y Cf. A154638, A169452, A170750.

%K nonn

%O 0,2

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