A162877 - OEIS

%I #18 Sep 08 2022 08:45:46

%S 1,40,1560,60060,2311920,88979280,3424561140,131801403240,

%T 5072652999960,195231667516860,7513899339838320,289188142406526480,

%U 11130010920731869140,428361764988438838440,16486399071025250766360

%N Number of reduced words of length n in Coxeter group on 40 generators S_i with relations (S_i)^2 = (S_i S_j)^3 = I.

%C The initial terms coincide with those of A170759, 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="/A162877/b162877.txt">Table of n, a(n) for n = 0..615</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (38, 38, -741).

%F G.f.: (t^3 + 2*t^2 + 2*t + 1)/(741*t^3 - 38*t^2 - 38*t + 1).

%F a(n) = 38*a(n-1) + 38*a(n-2) - 741*a(n-3), n > 0. - _Muniru A Asiru_, Oct 24 2018

%F G.f.: (1+x)*(1-x^3)/(1 - 39*x + 779*x^3 - 741*x^4). - _G. C. Greubel_, Apr 27 2019

%p seq(coeff(series((x^3+2*x^2+2*x+1)/(741*x^3-38*x^2-38*x+1),x,n+1), x, n), n = 0 .. 20); # _Muniru A Asiru_, Oct 24 2018

%t coxG[{3,741,-38}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jan 29 2017 *)

%t CoefficientList[Series[(t^3+2*t^2+2*t+1)/(741*t^3-38*t^2-38*t+1), {t, 0, 20}], t] (* _G. C. Greubel_, Oct 24 2018 *)

%o (PARI) my(t='t+O('t^20)); Vec((t^3+2*t^2+2*t+1)/(741*t^3-38*t^2-38*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)/(741*t^3-38*t^2-38*t+1))); // _G. C. Greubel_, Oct 24 2018

%o (GAP) a:=[40,1560,60060];; for n in [4..20] do a[n]:=38*a[n-1]+38*a[n-2] -741*a[n-3]; od; Concatenation([1],a); # _Muniru A Asiru_, Oct 24 2018

%o (Sage) ((1+x)*(1-x^3)/(1 -39*x +779*x^3 -741*x^4)).series(x, 20).coefficients(x, sparse=False) # _G. C. Greubel_, Apr 27 2019

%K nonn

%O 0,2

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