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A163441 Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

%I A163441 #20 Sep 08 2022 08:45:46
%S A163441 1,16,240,3600,54000,809880,12146400,182169120,2732133600,40975956000,
%T A163441 614548634280,9216869130000,138232634196720,2073183516810000,
%U A163441 31093163487414000,466328623499110680,6993897072666789600
%N A163441 Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.
%C A163441 The initial terms coincide with those of A170735, although the two sequences are eventually different.
%C A163441 Computed with MAGMA using commands similar to those used to compute A154638.
%H A163441 G. C. Greubel, <a href="/A163441/b163441.txt">Table of n, a(n) for n = 0..845</a>
%H A163441 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (14, 14, 14, 14, -105).
%F A163441 G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(105*t^5 - 14*t^4 - 14*t^3 - 14*t^2 - 14*t + 1).
%F A163441 a(n) = 14*a(n-1)+14*a(n-2)+14*a(n-3)+14*a(n-4)-105*a(n-5). - _Wesley Ivan Hurt_, May 10 2021
%t A163441 CoefficientList[Series[(1+x)*(1-x^5)/(1-15*x+119*x^5-105*x^6), {x, 0, 20}], x] (* or *) LinearRecurrence[{14, 14, 14, 14, -105}, {1, 16, 240, 3600, 54000, 809880}, 20] (* _G. C. Greubel_, Dec 23 2016 *)
%t A163441 coxG[{5, 105, -14}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, May 13 2019 *)
%o A163441 (PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-15*x+119*x^5-105*x^6)) \\ _G. C. Greubel_, Dec 23 2016
%o A163441 (Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-15*x+119*x^5-105*x^6) )); // _G. C. Greubel_, May 13 2019
%o A163441 (Sage) ((1+x)*(1-x^5)/(1-15*x+119*x^5-105*x^6)).series(x, 20).coefficients(x, sparse=False) # _G. C. Greubel_, May 13 2019
%K A163441 nonn
%O A163441 0,2
%A A163441 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009