A162889 - OEIS

%I #13 Sep 08 2022 08:45:46

%S 1,46,2070,92115,4098600,182342160,8112199590,360902223000,

%T 16056115855560,714317717862540,31779155482826400,1413817266133308960,

%U 62899068010426041240,2798305588240613272800,124493325781573753947360

%N Number of reduced words of length n in Coxeter group on 46 generators S_i with relations (S_i)^2 = (S_i S_j)^3 = I.

%C The initial terms coincide with those of A170765, 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="/A162889/b162889.txt">Table of n, a(n) for n = 0..605</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (44, 44, -990).

%F G.f.: (t^3 + 2*t^2 + 2*t + 1)/(990*t^3 - 44*t^2 - 44*t + 1).

%F From _G. C. Greubel_, Apr 28 2019: (Start)

%F a(n) = 44*a(n-1) + 44*a(n-2) - 990*a(n-3).

%F G.f.: (1+x)*(1-x^3)/(1 - 45*x + 1034*x^3 - 990*x^4). (End)

%t CoefficientList[Series[(t^3+2*t^2+2*t+1)/(990*t^3-44*t^2-44*t+1), {t, 0, 20}], t] (* _G. C. Greubel_, Oct 24 2018 *)

%t coxG[{3, 990, -44}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, Apr 28 2019 *)

%o (PARI) my(t='t+O('t^20)); Vec((t^3+2*t^2+2*t+1)/(990*t^3-44*t^2-44*t+1)) \\ _G. C. Greubel_, Oct 24 2018

%o (Magma) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!((t^3 + 2*t^2+2*t+1)/(990*t^3-44*t^2-44*t+1))); // _G. C. Greubel_, Oct 24 2018

%o (Sage) ((1+x)*(1-x^3)/(1-45*x+1034*x^3-990*x^4)).series(x, 20).coefficients(x, sparse=False) # _G. C. Greubel_, Apr 28 2019

%o (GAP) a:=[46,2070,92115];; for n in [4..20] do a[n]:=44*a[n-1]+44*a[n-2] - 990*a[n-3]; od; Concatenation([1], a); # _G. C. Greubel_, Apr 28 2019

%K nonn

%O 0,2

%A _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009