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A163231 Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.

%I A163231 #14 Sep 08 2022 08:45:46
%S A163231 1,45,1980,87120,3832290,168577200,7415481150,326196882000,
%T A163231 14348955088710,631190926398780,27765226324720170,1221354364616557380,
%U A163231 53725709508796162530,2363320544672336677560,103959241263364038810390
%N A163231 Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.
%C A163231 The initial terms coincide with those of A170764, although the two sequences are eventually different.
%C A163231 Computed with MAGMA using commands similar to those used to compute A154638.
%H A163231 G. C. Greubel, <a href="/A163231/b163231.txt">Table of n, a(n) for n = 0..600</a>
%H A163231 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (43, 43, 43, -946).
%F A163231 G.f.: (t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(946*t^4 - 43*t^3 - 43*t^2 - 43*t + 1).
%F A163231 a(n) = 43*a(n-1)+43*a(n-2)+43*a(n-3)-946*a(n-4). - _Wesley Ivan Hurt_, May 06 2021
%t A163231 CoefficientList[Series[(t^4+2*t^3+2*t^2+2*t+1)/(946*t^4-43*t^3-43*t^2 - 43*t+1), {t,0,20}], t] (* or *) Join[{1}, LinearRecurrence[ {43, 43, 43, -946}, {45,1980,87120,3832290}, 20]] (* _G. C. Greubel_, Dec 11 2016 *)
%t A163231 coxG[{4, 946, -43}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, Apr 30 2019 *)
%o A163231 (PARI) my(t='t+O('t^20)); Vec((t^4+2*t^3+2*t^2+2*t+1)/(946*t^4-43*t^3 - 43*t^2-43*t+1)) \\ _G. C. Greubel_, Dec 11 2016
%o A163231 (Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+x)*(1-x^4)/(1-44*x+989*x^4-946*x^5) )); // _G. C. Greubel_, Apr 30 2019
%o A163231 (Sage) ((1+x)*(1-x^4)/(1-44*x+989*x^4-946*x^5)).series(x, 30).coefficients(x, sparse=False) # _G. C. Greubel_, Apr 30 2019
%K A163231 nonn
%O A163231 0,2
%A A163231 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009