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 A165895 #17 Sep 08 2022 08:45:48
%S A165895 1,22,462,9702,203742,4278582,89850222,1886854662,39623947902,
%T A165895 832102905942,17474161024551,366957381510720,7706105011623480,
%U A165895 161828205241958640,3398392310036308200,71366238509821184160
%N A165895 Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.
%C A165895 The initial terms coincide with those of A170741, although the two sequences are eventually different.
%C A165895 Computed with MAGMA using commands similar to those used to compute A154638.
%H A165895 G. C. Greubel, <a href="/A165895/b165895.txt">Table of n, a(n) for n = 0..500</a>
%H A165895 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (20,20,20,20,20,20,20,20,20,-210).
%F A165895 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)/(210*t^10 - 20*t^9 - 20*t^8 - 20*t^7 - 20*t^6 - 20*t^5 - 20*t^4 - 20*t^3 - 20*t^2 - 20*t + 1).
%p A165895 seq(coeff(series((1+t)*(1-t^10)/(1-21*t+230*t^10-210*t^11), t, n+1), t, n), n = 0..20); # _G. C. Greubel_, Sep 25 2019
%t A165895 CoefficientList[Series[(1+t)*(1-t^10)/(1-21*t+230*t^10-210*t^11), {t, 0, 25}], t] (* _G. C. Greubel_, Apr 17 2016 *)
%t A165895 coxG[{10, 210, -20}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, Sep 25 2019 *)
%o A165895 (PARI) my(t='t+O('t^20)); Vec((1+t)*(1-t^10)/(1-21*t+230*t^10-210*t^11)) \\ _G. C. Greubel_, Sep 25 2019
%o A165895 (Magma) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^10)/(1-21*t+230*t^10-210*t^11) )); // _G. C. Greubel_, Sep 25 2019
%o A165895 (Sage)
%o A165895 def A165895_list(prec):
%o A165895 P.<t> = PowerSeriesRing(ZZ, prec)
%o A165895 return P((1+t)*(1-t^10)/(1-21*t+230*t^10-210*t^11)).list()
%o A165895 A165895_list(20) # _G. C. Greubel_, Sep 25 2019
%o A165895 (GAP) a:=[22, 462, 9702, 203742, 4278582, 89850222, 1886854662, 39623947902, 832102905942, 17474161024551];; for n in [11..25] do a[n]:=20*Sum([1..9], j-> a[n-j]) -210*a[n-10]; od; Concatenation([1], a); # _G. C. Greubel_, Sep 25 2019
%Y A165895 Cf. A154638, A170741.
%K A165895 nonn
%O A165895 0,2
%A A165895 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009