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A163991 Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.

%I A163991 #17 Sep 08 2022 08:45:47
%S A163991 1,23,506,11132,244904,5387888,118533283,2607726660,57369864321,
%T A163991 1262134326684,27766896042732,610870411765152,13439120433048156,
%U A163991 295660019761129485,6504506579923898238,143098839952914095019,3148167773259336785958,69259543486514630343864
%N A163991 Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.
%C A163991 The initial terms coincide with those of A170742, although the two sequences are eventually different.
%C A163991 Computed with MAGMA using commands similar to those used to compute A154638.
%H A163991 G. C. Greubel, <a href="/A163991/b163991.txt">Table of n, a(n) for n = 0..740</a>
%H A163991 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (21,21,21,21,21,-231).
%F A163991 G.f.: (t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(231*t^6 - 21*t^5 - 21*t^4 - 21*t^3 - 21*t^2 - 21*t + 1).
%F A163991 G.f.: (1+x)*(1-x^6)/(1 -22*x +252*x^6 -231*x^7). - _G. C. Greubel_, Apr 25 2019
%t A163991 CoefficientList[Series[(1+x)*(1-x^6)/(1-22*x+252*x^6-231*x^7), {x,0,20}], x] (* _G. C. Greubel_, Aug 24 2017, modified Apr 25 2019 *)
%t A163991 coxG[{6, 231, -21}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, Apr 25 2019 *)
%o A163991 (PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^6)/(1-22*x+252*x^6-231*x^7)) \\ _G. C. Greubel_, Aug 24 2017, modified Apr 25 2019
%o A163991 (Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^6)/(1-22*x+252*x^6-231*x^7) )); // _G. C. Greubel_, Apr 25 2019
%o A163991 (Sage) ((1+x)*(1-x^6)/(1-22*x+252*x^6-231*x^7)).series(x, 20).coefficients(x, sparse=False) # _G. C. Greubel_, Apr 25 2019
%K A163991 nonn
%O A163991 0,2
%A A163991 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009