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%I #17 Sep 08 2022 08:45:48
%S 1,21,420,8400,168000,3360000,67200000,1344000000,26880000000,
%T 537600000000,10751999999790,215039999991600,4300799999748210,
%U 86015999993288400,1720319999832252000,34406399995974720000
%N Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.
%C The initial terms coincide with those of A170740, 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="/A165894/b165894.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 (19,19,19,19,19,19,19,19,19,-190).
%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)/(190*t^10 - 19*t^9 - 19*t^8 - 19*t^7 - 19*t^6 - 19*t^5 - 19*t^4 - 19*t^3 - 19*t^2 - 19*t + 1).
%p seq(coeff(series((1+t)*(1-t^10)/(1-20*t+209*t^10-190*t^11), t, n+1), t, n), n = 0..20); # _G. C. Greubel_, Sep 24 2019
%t CoefficientList[Series[(1+t)*(1-t^10)/(1-20*t+209*t^10-190*t^11), {t, 0, 20}], t] (* _G. C. Greubel_, Apr 17 2016 *)
%t coxG[{10, 190, -19}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, Sep 24 2019 *)
%o (PARI) my(t='t+O('t^20)); Vec((1+t)*(1-t^10)/(1-20*t+209*t^10-190*t^11)) \\ _G. C. Greubel_, Sep 24 2019
%o (Magma) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^10)/(1-20*t+209*t^10-190*t^11) )); // _G. C. Greubel_, Sep 24 2019
%o (Sage)
%o def A165894_list(prec):
%o P.<t> = PowerSeriesRing(ZZ, prec)
%o return P((1+t)*(1-t^10)/(1-20*t+209*t^10-190*t^11)).list()
%o A165894_list(30) # _G. C. Greubel_, Sep 24 2019
%o (GAP) a:=[21, 420, 8400, 168000, 3360000, 67200000, 1344000000, 26880000000, 537600000000, 10751999999790];; for n in [7..30] do a[n]:=19*Sum([1..9], j-> a[n-j]) -190*a[n-10]; od; Concatenation([1], a); # _G. C. Greubel_, Sep 24 2019
%Y Cf. A154638, A170740.
%K nonn
%O 0,2
%A _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009