# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/

Search: id:a166421
Showing 1-1 of 1

%I A166421 #16 Jul 25 2024 14:48:42
%S A166421 1,27,702,18252,474552,12338352,320797152,8340725952,216858874752,
%T A166421 5638330743552,146596599332352,3811511582640801,99099301148651700,
%U A166421 2576581829864707275,66991127576476229100,1741769316988221795300
%N A166421 Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.
%C A166421 The initial terms coincide with those of A170746, although the two sequences are eventually different.
%C A166421 Computed with MAGMA using commands similar to those used to compute A154638.
%H A166421 G. C. Greubel, <a href="/A166421/b166421.txt">Table of n, a(n) for n = 0..500</a>
%H A166421 <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (25,25,25,25,25,25,25,25,25,25,-325).
%F A166421 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)/(325*t^11 - 25*t^10 - 25*t^9 - 25*t^8 - 25*t^7 - 25*t^6 - 25*t^5 - 25*t^4 - 25*t^3 - 25*t^2 - 25*t + 1).
%F A166421 From _G. C. Greubel_, Jan 17 2023: (Start)
%F A166421 a(n) = 25*Sum_{j=1..10} a(n-j) - 325*a(n-11).
%F A166421 G.f.: (1+x)*(1-x^11)/(1 - 26*x + 350*x^11 - 325*x^12). (End)
%t A166421 With[{p=325, q=25}, 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 A166421 coxG[{11,325,-25}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, May 22 2021 *)
%o A166421 (Magma)
%o A166421 R<x>:=PowerSeriesRing(Integers(), 30);
%o A166421 Coefficients(R!( (1+x)*(1-x^11)/(1-26*x+350*x^11-325*x^12) )); // _G. C. Greubel_, Jul 25 2024
%o A166421 (SageMath)
%o A166421 def A166421_list(prec):
%o A166421     P.<x> = PowerSeriesRing(ZZ, prec)
%o A166421     return P( (1+x)*(1-x^11)/(1-26*x+350*x^11-325*x^12) ).list()
%o A166421 A166421_list(30) # _G. C. Greubel_, Jul 25 2024
%Y A166421 Cf. A154638, A169452, A170746.
%K A166421 nonn
%O A166421 0,2
%A A166421 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009

# Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE