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A164330 Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.

%I A164330 #16 Sep 08 2022 08:45:47
%S A164330 1,45,1980,87120,3833280,168664320,7421229090,326534036400,
%T A164330 14367495685950,632169725893200,27815464230602400,1223880262963776000,
%U A164330 53850724390367020710,2369431557254469630780,104254974618644628784170
%N A164330 Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.
%C A164330 The initial terms coincide with those of A170764, although the two sequences are eventually different.
%C A164330 Computed with MAGMA using commands similar to those used to compute A154638.
%H A164330 G. C. Greubel, <a href="/A164330/b164330.txt">Table of n, a(n) for n = 0..600</a>
%H A164330 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (43, 43, 43, 43, 43, -946).
%F A164330 G.f.: (t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(946*t^6 - 43*t^5 - 43*t^4 - 43*t^3 - 43*t^2 - 43*t + 1).
%F A164330 G.f.: (1+x)*(1-x^6)/(1 -44*x +989*x^6 -946*x^7). - _G. C. Greubel_, Apr 25 2019
%F A164330 a(n) = -946*a(n-6) + 43*Sum_{k=1..5} a(n-k). - _Wesley Ivan Hurt_, May 06 2021
%t A164330 CoefficientList[Series[(1+x)*(1-x^6)/(1-44*x+989*x^6-946*x^7), {x,0,20}], x] (* _G. C. Greubel_, Sep 14 2017, modified Apr 25 2019 *)
%t A164330 coxG[{6, 946, -43}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, Apr 25 2019 *)
%o A164330 (PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^6)/(1-44*x+989*x^6-946*x^7)) \\ _G. C. Greubel_, Sep 14 2017, modified Apr 25 2019
%o A164330 (Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^6)/(1-44*x+989*x^6-946*x^7) )); // _G. C. Greubel_, Apr 25 2019
%o A164330 (Sage) ((1+x)*(1-x^6)/(1-44*x+989*x^6-946*x^7)).series(x, 20).coefficients(x, sparse=False) # _G. C. Greubel_, Apr 25 2019
%K A164330 nonn
%O A164330 0,2
%A A164330 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009