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 A165515 #14 Sep 08 2022 08:45:47
%S A165515 1,30,870,25230,731670,21218430,615334470,17844699630,517496289270,
%T A165515 15007392388395,435214379250840,12621216997908960,366015292928763240,
%U A165515 10614443494626832560,307818861335266403640,8926746978464285228160
%N A165515 Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^9 = I.
%C A165515 The initial terms coincide with those of A170749, although the two sequences are eventually different.
%C A165515 Computed with MAGMA using commands similar to those used to compute A154638.
%H A165515 G. C. Greubel, <a href="/A165515/b165515.txt">Table of n, a(n) for n = 0..682</a>
%H A165515 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (28,28,28,28,28,28,28,28,-406).
%F A165515 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)/( 406*t^9 -28*t^8 -28*t^7 -28*t^6 -28*t^5 -28*t^4 -28*t^3 -28*t^2 -28*t + 1).
%p A165515 seq(coeff(series((1+t)*(1-t^9)/(1-29*t+434*t^9-406*t^10), t, n+1), t, n), n = 0 .. 20); # _G. C. Greubel_, Sep 16 2019
%t A165515 CoefficientList[Series[(1+t)*(1-t^9)/(1-29*t+434*t^9-406*t^10), {t,0,20}], t] (* _G. C. Greubel_, Oct 21 2018 *)
%t A165515 coxG[{9, 406, -28}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, Sep 16 2019 *)
%o A165515 (PARI) my(t='t+O('t^20)); Vec((1+t)*(1-t^9)/(1-29*t+434*t^9-406*t^10)) \\ _G. C. Greubel_, Oct 21 2018
%o A165515 (Magma) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^9)/(1-29*t+434*t^9-406*t^10) )); // _G. C. Greubel_, Oct 21 2018
%o A165515 (Sage)
%o A165515 def A165515_list(prec):
%o A165515 P.<t> = PowerSeriesRing(ZZ, prec)
%o A165515 return P((1+t)*(1-t^9)/(1-29*t+434*t^9-406*t^10)).list()
%o A165515 A165515_list(20) # _G. C. Greubel_, Sep 16 2019
%o A165515 (GAP) a:=[30, 870, 25230, 731670, 21218430, 615334470, 17844699630, 517496289270, 15007392388395];; for n in [10..20] do a[n]:=28*Sum([1..8], j-> a[n-j]) -406*a[n-6]; od; Concatenation([1], a); # _G. C. Greubel_, Sep 16 2019
%K A165515 nonn
%O A165515 0,2
%A A165515 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009