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A166419 Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.

%I A166419 #14 Jul 25 2024 02:33:41
%S A166419 1,25,600,14400,345600,8294400,199065600,4777574400,114661785600,
%T A166419 2751882854400,66045188505600,1585084524134100,38042028579211200,
%U A166419 913008685900896300,21912208461617371200,525893003078717548800
%N A166419 Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.
%C A166419 The initial terms coincide with those of A170744, although the two sequences are eventually different.
%C A166419 Computed with MAGMA using commands similar to those used to compute A154638.
%H A166419 G. C. Greubel, <a href="/A166419/b166419.txt">Table of n, a(n) for n = 0..500</a>
%H A166419 <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (23,23,23,23,23,23,23,23,23,23,-276).
%F A166419 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)/(276*t^11 - 23*t^10 - 23*t^9 - 23*t^8 - 23*t^7 - 23*t^6 - 23*t^5 - 23*t^4 - 23*t^3 - 23*t^2 - 23*t + 1).
%F A166419 From _G. C. Greubel_, Jul 23 2024: (Start)
%F A166419 a(n) = 23*Sum_{j=1..10} a(n-j) - 276*a(n-11).
%F A166419 G.f.: (1+x)*(1-x^11)/(1 - 24*x + 299*x^11 - 276*x^12). (End)
%t A166419 With[{p=276, q=23}, 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 23 2024 *)
%t A166419 coxG[{11, 276, -23, 30}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, Jul 23 2024 *)
%o A166419 (Magma)
%o A166419 R<x>:=PowerSeriesRing(Integers(), 30);
%o A166419 Coefficients(R!( (1+x)*(1-x^11)/(1-24*x+299*x^11-276*x^12) )); // _G. C. Greubel_, Jul 23 2024
%o A166419 (SageMath)
%o A166419 def A166419_list(prec):
%o A166419     P.<x> = PowerSeriesRing(ZZ, prec)
%o A166419     return P( (1+x)*(1-x^11)/(1-24*x+299*x^11-276*x^12) ).list()
%o A166419 A166419_list(30) # _G. C. Greubel_, Jul 23 2024
%Y A166419 Cf. A154638, A169452, A170744.
%K A166419 nonn
%O A166419 0,2
%A A166419 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009