%I #15 Sep 08 2022 08:45:48
%S 1,9,72,576,4608,36864,294912,2359296,18874368,150994944,1207959516,
%T 9663675840,77309404452,618475217472,4947801594624,39582411595776,
%U 316659283476480,2533274193494016,20266192953409536,162129538870935552
%N Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.
%C The initial terms coincide with those of A003951, 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="/A165787/b165787.txt">Table of n, a(n) for n = 0..500</a>
%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (7,7,7,7,7,7,7,7,7,-28).
%F G.f.: (t^10 + 2*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)/(28*t^10 - 7*t^9 - 7*t^8 - 7*t^7 - 7*t^6 - 7*t^5 - 7*t^4 - 7*t^3 - 7*t^2 - 7*t + 1).
%p seq(coeff(series((1+t)*(1-t^10)/(1-8*t+35*t^10-28*t^11), t, n+1), t, n), n = 0..20); # _G. C. Greubel_, Aug 10 2019
%t CoefficientList[Series[(1+t)*(1-t^10)/(1-8*t+35*t^10-28*t^11), {t, 0, 20}], t] (* _G. C. Greubel_, Apr 08 2016 *)
%t coxG[{10, 28, -7}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, Sep 22 2019 *)
%o (PARI) my(t='t+O('t^20)); Vec((1+t)*(1-t^10)/(1-8*t+35*t^10-28*t^11)) \\ _G. C. Greubel_, Sep 22 2019
%o (Magma) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^10)/(1-8*t+35*t^10-28*t^11) )); // _G. C. Greubel_, Sep 22 2019
%o (Sage)
%o def A165787_list(prec):
%o P.<t> = PowerSeriesRing(ZZ, prec)
%o return P((1+t)*(1-t^10)/(1-8*t+35*t^10-28*t^11)).list()
%o A165787_list(20) # _G. C. Greubel_, Sep 22 2019
%o (GAP) a:=[9, 72, 576, 4608, 36864, 294912, 2359296, 18874368, 150994944, 1207959516];; for n in [11..20] do a[n]:=7*Sum([1..9], j-> a[n-j]) -28*a[n-10]; od; Concatenation([1], a); # _G. C. Greubel_, Sep 22 2019
%K nonn
%O 0,2
%A _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009