%I #10 Sep 08 2022 08:45:47

%S 1,12,132,1452,15972,175692,1932612,21258732,233846052,2572306506,

%T 28295370840,311249071320,3423739697400,37661135713080,

%U 414272482302360,4556997189369240,50126967807537720,551396631852151800

%N Number of reduced words of length n in Coxeter group on 12 generators S_i with relations (S_i)^2 = (S_i S_j)^9 = I.

%C The initial terms coincide with those of A003954, 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="/A165266/b165266.txt">Table of n, a(n) for n = 0..955</a>

%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (10,10,10,10,10,10,10,10,-55).

%F G.f.: (t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(55*t^9 - 10*t^8 - 10*t^7 - 10*t^6 - 10*t^5 - 10*t^4 - 10*t^3 - 10*t^2 - 10*t + 1).

%p seq(coeff(series((1+t)*(1-t^9)/(1-11*t+65*t^9-55*t^10), t, n+1), t, n), n = 0..30); # _G. C. Greubel_, Sep 25 2019

%t CoefficientList[Series[(1+t)*(1-t^9)/(1-11*t+65*t^9-55*t^10), {t,0,30}], t] (* or *) coxG[{9, 55, -10}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, Sep 25 2019 *)

%o (PARI) my(t='t+O('t^30)); Vec((1+t)*(1-t^9)/(1-11*t+65*t^9-55*t^10)) \\ _G. C. Greubel_, Sep 25 2019

%o (Magma) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^9)/(1-11*t+65*t^9-55*t^10) )); // _G. C. Greubel_, Sep 25 2019

%o (Sage)

%o def A165266_list(prec):

%o P.<t> = PowerSeriesRing(ZZ, prec)

%o return P((1+t)*(1-t^9)/(1-11*t+65*t^9-55*t^10)).list()

%o A165266_list(30) # _G. C. Greubel_, Sep 25 2019

%o (GAP) a:=[12, 132, 1452, 15972, 175692, 1932612, 21258732, 233846052, 2572306506];; for n in [10..30] do a[n]:=10*Sum([1..8], j-> a[n-j]) -55*a[n-9]; od; Concatenation([1], a); # _G. C. Greubel_, Sep 25 2019

%K nonn

%O 0,2

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