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A162882 Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^3 = I.

%I A162882 #18 Sep 08 2022 08:45:46
%S A162882 1,44,1892,80410,3416952,145180728,6168492330,262088760780,
%T A162882 11135706433236,473137249574682,20102798001348216,854133737629549608,
%U A162882 36290691560131770762,1541929835910758016492,65513979388697887768644
%N A162882 Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^3 = I.
%C A162882 The initial terms coincide with those of A170763, although the two sequences are eventually different.
%C A162882 Computed with MAGMA using commands similar to those used to compute A154638.
%H A162882 G. C. Greubel, <a href="/A162882/b162882.txt">Table of n, a(n) for n = 0..612</a>
%H A162882 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (42, 42, -903).
%F A162882 G.f.: (t^3 + 2*t^2 + 2*t + 1)/(903*t^3 - 42*t^2 - 42*t + 1).
%F A162882 a(n) = 42*a(n-1) + 42*a(n-2) - 903*a(n-3), n > 0. - _Muniru A Asiru_, Oct 24 2018
%F A162882 G.f.: (1+x)*(1-x^3)/(1 - 43*x + 945*x^3 - 903*x^4). - _G. C. Greubel_, Apr 27 2019
%p A162882 seq(coeff(series((x^3+2*x^2+2*x+1)/(903*x^3-42*x^2-42*x+1),x,n+1), x, n), n = 0 .. 20); # _Muniru A Asiru_, Oct 24 2018
%t A162882 CoefficientList[Series[(t^3+2*t^2+2*t+1)/(903*t^3-42*t^2-42*t+1), {t, 0, 20}], t] (* _G. C. Greubel_, Oct 24 2018 *)
%t A162882 coxG[{3, 903, -42}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, Apr 27 2019 *)
%o A162882 (PARI) my(t='t+O('t^20)); Vec((t^3+2*t^2+2*t+1)/(903*t^3-42*t^2-42*t+1)) \\ _G. C. Greubel_, Oct 24 2018
%o A162882 (Magma) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!((t^3 + 2*t^2+2*t+1)/(903*t^3-42*t^2-42*t+1))); // _G. C. Greubel_, Oct 24 2018
%o A162882 (GAP) a:=[44,1892,80410];; for n in [4..20] do a[n]:=42*a[n-1]+42*a[n-2] -903*a[n-3]; od; Concatenation([1],a); # _Muniru A Asiru_, Oct 24 2018
%o A162882 (Sage) ((1+x)*(1-x^3)/(1 -43*x +945*x^3 -903*x^4)).series(x, 20).coefficients(x, sparse=False) # _G. C. Greubel_, Apr 27 2019
%K A162882 nonn,easy
%O A162882 0,2
%A A162882 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009