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A166608 Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^12 = I.

%I A166608 #17 Sep 08 2022 08:45:48
%S A166608 1,22,462,9702,203742,4278582,89850222,1886854662,39623947902,
%T A166608 832102905942,17474161024782,366957381520422,7706105011928631,
%U A166608 161828205250496400,3398392310260322760,71366238515464643520
%N A166608 Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^12 = I.
%C A166608 The initial terms coincide with those of A170741, although the two sequences are eventually different.
%C A166608 Computed with MAGMA using commands similar to those used to compute A154638.
%H A166608 G. C. Greubel, <a href="/A166608/b166608.txt">Table of n, a(n) for n = 0..500</a>
%H A166608 <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, -210).
%F A166608 G.f.: (t^12 + 2*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)/(210*t^12 - 20*t^11 - 20*t^10 - 20*t^9 -20*t^8 -20*t^7 - 20*t^6 - 20*t^5 - 20*t^4 - 20*t^3 - 20*t^2 -20*t + 1).
%F A166608 G.f.: (1+x)*(1-x^12)/(1 -21*x +230*x^12 -210*x^13). - _G. C. Greubel_, Apr 25 2019
%t A166608 CoefficientList[Series[(1+x)*(1-x^12)/(1 -21*x +230*x^12 -210*x^13), {x, 0, 20}], x] (* _G. C. Greubel_, May 18 2016, modified Apr 25 2019 *)
%t A166608 coxG[{12,210,-20}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jul 20 2018 *)
%o A166608 (PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^12)/(1 -21*x +230*x^12 -210*x^13)) \\ _G. C. Greubel_, Apr 25 2019
%o A166608 (Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^12)/(1 -21*x +230*x^12 -210*x^13) )); // _G. C. Greubel_, Apr 25 2019
%o A166608 (Sage) ((1+x)*(1-x^12)/(1 -21*x +230*x^12 -210*x^13)).series(x, 20).coefficients(x, sparse=False) # _G. C. Greubel_, Apr 25 2019
%K A166608 nonn
%O A166608 0,2
%A A166608 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009