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%I #12 Sep 08 2022 08:45:46
%S 1,15,210,2835,38220,514605,6928740,93285465,1255955610,16909618635,
%T 227663487870,3065158424055,41267909559240,555612506386665,
%U 7480515990707760,100714290692336685,1355971748798391270
%N Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^3 = I.
%C The initial terms coincide with those of A170734, although the two sequences are eventually different.
%C Computed with MAGMA using commands similar to those used to compute A154638.
%H G. C. Greubel, <a href="/A162785/b162785.txt">Table of n, a(n) for n = 0..880</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (13, 13, -91).
%F G.f.: (t^3 + 2*t^2 + 2*t + 1)/(91*t^3 - 13*t^2 - 13*t + 1).
%F G.f.: (1+x)*(1-x^3)/(1 - 14*x + 104*x^3 - 91*x^4). - _G. C. Greubel_, Apr 26 2019
%t CoefficientList[Series[(1+x)*(1-x^3)/(1-14*x+104*x^3-91*x^4), {x, 0, 20}], x] (* or *) coxG[{3, 91, -13}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, Apr 26 2019 *)
%o (PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^3)/(1-14*x+104*x^3-91*x^4)) \\ _G. C. Greubel_, Apr 26 2019
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^3)/(1-14*x+104*x^3-91*x^4) )); // _G. C. Greubel_, Apr 26 2019
%o (Sage) ((1+x)*(1-x^3)/(1-14*x+104*x^3-91*x^4)).series(x, 20).coefficients(x, sparse=False) # _G. C. Greubel_, Apr 26 2019
%o (GAP) a:=[15, 210, 2835];; for n in [4..20] do a[n]:=13*a[n-1]+13*a[n-2] -91*a[n-3]; od; Concatenation([1], a); # _G. C. Greubel_, Apr 26 2019
%K nonn
%O 0,2
%A _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009
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