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 A164610 #20 Sep 08 2022 08:45:47
%S A164610 1,13,156,1872,22464,269568,3234816,38817714,465811632,5589728430,
%T A164610 67076607312,804917681568,9658992904704,115907683567104,
%U A164610 1390889427339126,16690639822542972,200287278204994266
%N A164610 Number of reduced words of length n in Coxeter group on 13 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I.
%C A164610 The initial terms coincide with those of A170732, although the two sequences are eventually different.
%C A164610 Computed with MAGMA using commands similar to those used to compute A154638.
%H A164610 G. C. Greubel, <a href="/A164610/b164610.txt">Table of n, a(n) for n = 0..920</a>
%H A164610 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (11,11,11,11,11,11,-66).
%F A164610 G.f.: (t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(66*t^7 - 11*t^6 - 11*t^5 - 11*t^4 - 11*t^3 - 11*t^2 - 11*t + 1).
%F A164610 a(n) = -66*a(n-7) + 11*Sum_{k=1..6} a(n-k). - _Wesley Ivan Hurt_, May 11 2021
%p A164610 seq(coeff(series((1+t)*(1-t^7)/(1-12*t+77*t^7-66*t^8), t, n+1), t, n), n = 0..20); # _G. C. Greubel_, Sep 15 2019
%t A164610 CoefficientList[Series[(1+t)*(1-t^7)/(1-12*t+77*t^7-66*t^8), {t, 0, 20}], t] (* _G. C. Greubel_, Aug 10 2017 *)
%t A164610 coxG[{7, 6, -11}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, Sep 15 2019 *)
%o A164610 (PARI) my(t='t+O('t^20)); Vec((1+t)*(1-t^7)/(1-12*t+77*t^7-66*t^8)) \\ _G. C. Greubel_, Aug 10 2017
%o A164610 (Magma) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^7)/(1-12*t+77*t^7-66*t^8) )); // _G. C. Greubel_, Sep 15 2019
%o A164610 (Sage)
%o A164610 def A164610_list(prec):
%o A164610 P.<t> = PowerSeriesRing(ZZ, prec)
%o A164610 return P((1+t)*(1-t^7)/(1-12*t+77*t^7-66*t^8)).list()
%o A164610 A164610_list(20) # _G. C. Greubel_, Sep 15 2019
%o A164610 (GAP) a:=[13,156,1872,22464,269568,3234816,38817714];; for n in [8..20] do a[n]:=11*(a[n-1] +a[n-2]+a[n-3]+a[n-4]+a[n-5]+a[n-6]) -66*a[n-7]; od; Concatenation([1], a); # _G. C. Greubel_, Sep 15 2019
%K A164610 nonn
%O A164610 0,2
%A A164610 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009