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 A165873 #17 Sep 08 2022 08:45:48
%S A165873 1,13,156,1872,22464,269568,3234816,38817792,465813504,5589762048,
%T A165873 67077144498,804925733040,9659108785326,115909305290064,
%U A165873 1390911661874592,16690939923220992,200291278847362560
%N A165873 Number of reduced words of length n in Coxeter group on 13 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.
%C A165873 The initial terms coincide with those of A170732, although the two sequences are eventually different.
%C A165873 Computed with MAGMA using commands similar to those used to compute A154638.
%H A165873 G. C. Greubel, <a href="/A165873/b165873.txt">Table of n, a(n) for n = 0..500</a>
%H A165873 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (11,11,11,11,11,11,11,11,11,-66).
%F A165873 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)/(66*t^10 - 11*t^9 - 11*t^8 - 11*t^7 - 11*t^6 - 11*t^5 - 11*t^4 - 11*t^3 - 11*t^2 - 11*t + 1).
%p A165873 seq(coeff(series((1+t)*(1-t^10)/(1-12*t+77*t^10-66*t^11), t, n+1), t, n), n = 0 .. 30); # _G. C. Greubel_, Sep 23 2019
%t A165873 coxG[{10,66,-11}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jun 12 2015 *)
%t A165873 CoefficientList[Series[(1+t)*(1-t^10)/(1-12*t+77*t^10-66*t^11), {t, 0, 30}], t] (* _G. C. Greubel_, Sep 23 2019 *)
%o A165873 (PARI) my(t='t+O('t^30)); Vec((1+t)*(1-t^10)/(1-12*t+77*t^10-66*t^11)) \\ _G. C. Greubel_, Sep 23 2019
%o A165873 (Magma) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^10)/(1-12*t+77*t^10-66*t^11) )); // _G. C. Greubel_, Sep 23 2019
%o A165873 (Sage)
%o A165873 def A165873_list(prec):
%o A165873 P.<t> = PowerSeriesRing(ZZ, prec)
%o A165873 return P((1+t)*(1-t^10)/(1-12*t+77*t^10-66*t^11)).list()
%o A165873 A165873_list(30) # _G. C. Greubel_, Sep 23 2019
%o A165873 (GAP) a:=[13, 156, 1872, 22464, 269568, 3234816, 38817792, 465813504, 5589762048, 67077144498];; for n in [7..30] do a[n]:=11*Sum([1..9], j-> a[n-j]) -66*a[n-10]; od; Concatenation([1], a); # _G. C. Greubel_, Sep 23 2019
%K A165873 nonn
%O A165873 0,2
%A A165873 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009