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A164369 Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I.

%I A164369 #16 Sep 08 2022 08:45:47
%S A164369 1,7,42,252,1512,9072,54432,326571,1959300,11755065,70525980,
%T A164369 423129420,2538617760,15230754000,91378809060,548238566925,
%U A164369 3289225689750,19734119944875,118397314970550,710339464409400,4261770250642800
%N A164369 Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I.
%C A164369 The initial terms coincide with those of A003949, although the two sequences are eventually different.
%C A164369 Computed with MAGMA using commands similar to those used to compute A154638.
%H A164369 G. C. Greubel, <a href="/A164369/b164369.txt">Table of n, a(n) for n = 0..1000</a>
%H A164369 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (5, 5, 5, 5, 5, 5, -15).
%F A164369 G.f.: (t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(15*t^7 - 5*t^6 - 5*t^5 - 5*t^4 - 5*t^3 - 5*t^2 - 5*t + 1).
%F A164369 G.f.: (1+x)*(1-x^7)/(1 -6*x +20*x^7 -15*x^8). - _G. C. Greubel_, Apr 25 2019
%t A164369 CoefficientList[Series[(1+x)*(1-x^7)/(1-6*x+20*x^7-15*x^8), {x, 0, 30}], x] (* _G. C. Greubel_, Sep 17 2017, modified Apr 25 2019 *)
%t A164369 coxG[{7, 15, -5, 30}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, Apr 25 2019 *)
%o A164369 (PARI) my(x='x+O('x^30)); Vec((1+x)*(1-x^7)/(1-6*x+20*x^7-15*x^8)) \\ _G. C. Greubel_, Sep 17 2017, modified Apr 25 2019
%o A164369 (Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+x)*(1-x^7)/(1-6*x+20*x^7-15*x^8) )); // _G. C. Greubel_, Apr 25 2019
%o A164369 (Sage) ((1+x)*(1-x^7)/(1-6*x+20*x^7-15*x^8)).series(x, 30).coefficients(x, sparse=False) # _G. C. Greubel_, Apr 25 2019
%K A164369 nonn
%O A164369 0,2
%A A164369 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009