This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A165786 #17 Sep 08 2022 08:45:48
%S A165786 1,8,56,392,2744,19208,134456,941192,6588344,46118408,322828828,
%T A165786 2259801600,15818609856,110730259584,775111751232,5425781797632,
%U A165786 37980469356480,265863262906752,1861042682227008,13027297668747264
%N A165786 Number of reduced words of length n in Coxeter group on 8 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.
%C A165786 The initial terms coincide with those of A003950, although the two sequences are eventually different.
%C A165786 Computed with MAGMA using commands similar to those used to compute A154638.
%H A165786 G. C. Greubel, <a href="/A165786/b165786.txt">Table of n, a(n) for n = 0..500</a>
%H A165786 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (6,6,6,6,6,6,6,6,6,-21).
%F A165786 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)/(21*t^10 - 6*t^9 - 6*t^8 - 6*t^7 - 6*t^6 - 6*t^5 - 6*t^4 - 6*t^3 - 6*t^2 - 6*t + 1).
%p A165786 seq(coeff(series((1+t)*(1-t^10)/(1-7*t+27*t^10-21*t^11), t, n+1), t, n), n = 0..20); # _G. C. Greubel_, Sep 22 2019
%t A165786 With[{num=Total[2t^Range[9]]+t^10+1,den=Total[-6 t^Range[9]]+21t^10+1}, CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Oct 20 2011 *)
%t A165786 CoefficientList[Series[(1+t)*(1-t^10)/(1-7*t+27*t^10-21*t^11), {t,0,20}], t] (* or *) coxG[{10, 21, -6}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, Sep 22 2019 *)
%o A165786 (PARI) my(t='t+O('t^20)); Vec((1+t)*(1-t^10)/(1-7*t+27*t^10-21*t^11)) \\ _G. C. Greubel_, Sep 22 2019
%o A165786 (Magma) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^10)/(1-7*t+27*t^10-21*t^11) )); // _G. C. Greubel_, Sep 22 2019
%o A165786 (Sage)
%o A165786 def A165786_list(prec):
%o A165786 P.<t> = PowerSeriesRing(ZZ, prec)
%o A165786 return P( (1+t)*(1-t^10)/(1-7*t+27*t^10-21*t^11) ).list()
%o A165786 A165786_list(30) # _G. C. Greubel_, Sep 22 2019
%o A165786 (GAP) a:=[8, 56, 392, 2744, 19208, 134456, 941192, 6588344, 46118408, 322828828];; for n in [11..20] do a[n]:=6*Sum([1..9], j-> a[n-j]) -21*a[n-10]; od; Concatenation([1], a); # _G. C. Greubel_, Sep 22 2019
%K A165786 nonn
%O A165786 0,2
%A A165786 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009