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A162885 Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^3 = I. 1

%I #15 Sep 08 2022 08:45:46

%S 1,45,1980,86130,3746160,162915390,7084967670,308115104220,

%T 13399485132330,582724430755830,25341851494598760,1102080851855063190,

%U 47927918932540448670,2084316599215116583020,90643945794494362584930

%N Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^3 = I.

%C The initial terms coincide with those of A170764, 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="/A162885/b162885.txt">Table of n, a(n) for n = 0..609</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (43, 43, -946).

%F G.f.: (t^3 + 2*t^2 + 2*t + 1)/(946*t^3 - 43*t^2 - 43*t + 1).

%F a(n) = 43*a(n-1) + 43*a(n-2) - 946*a(n-3), n > 0. - _Muniru A Asiru_, Oct 24 2018

%F G.f.: (1+x)*(1-x^3)/(1 - 44*x + 990*x^3 - 946*x^4). - _G. C. Greubel_, Apr 28 2019

%p seq(coeff(series((x^3+2*x^2+2*x+1)/(946*x^3-43*x^2-43*x+1),x,n+1), x, n), n = 0 .. 20); # _Muniru A Asiru_, Oct 24 2018

%t CoefficientList[Series[(t^3+2*t^2+2*t+1)/(946*t^3-43*t^2-43*t+1), {t, 0, 20}], t] (* _G. C. Greubel_, Oct 24 2018 *)

%t coxG[{3, 946, -43}] (* 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)/(946*t^3-43*t^2-43*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)/(946*t^3-43*t^2-43*t+1))); // _G. C. Greubel_, Oct 24 2018

%o (GAP) a:=[45,1980,86130];; for n in [4..20] do a[n]:=43*a[n-1]+43*a[n-2] -946*a[n-3]; od; Concatenation([1],a); # _Muniru A Asiru_, Oct 24 2018

%o (Sage) ((1+x)*(1-x^3)/(1-44*x+990*x^3-946*x^4)).series(x, 20).coefficients(x, sparse=False) # _G. C. Greubel_, Apr 28 2019

%K nonn

%O 0,2

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

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Last modified March 29 10:44 EDT 2024. Contains 371268 sequences. (Running on oeis4.)