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 A167919 #26 Sep 21 2023 02:08:36
%S A167919 1,13,156,1872,22464,269568,3234816,38817792,465813504,5589762048,
%T A167919 67077144576,804925734912,9659108818944,115909305827328,
%U A167919 1390911669927936,16690940039135232,200291280469622706
%N A167919 Number of reduced words of length n in Coxeter group on 13 generators S_i with relations (S_i)^2 = (S_i S_j)^16 = I.
%C A167919 The initial terms coincide with those of A170732, although the two sequences are eventually different.
%C A167919 Computed with MAGMA using commands similar to those used to compute A154638.
%H A167919 G. C. Greubel, <a href="/A167919/b167919.txt">Table of n, a(n) for n = 0..500</a>
%H A167919 <a href="/index/Rec#order_16">Index entries for linear recurrences with constant coefficients</a>, signature (11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,-66).
%F A167919 G.f.: (t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*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^16 - 11*t^15 - 11*t^14 - 11*t^13 - 11*t^12 - 11*t^11 - 11*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).
%F A167919 From _G. C. Greubel_, Sep 13 2023: (Start)
%F A167919 G.f.: (1+t)*(1-t^16)/(1 - 12*t + 77*t^16 - 66*t^17).
%F A167919 a(n) = 11*Sum_{j=1..15} a(n-j) - 66*a(n-16). (End)
%t A167919 CoefficientList[Series[(1+t)*(1-t^16)/(1-12*t+77*t^16-66*t^17), {t, 0, 50}], t] (* _G. C. Greubel_, Jul 01 2016; Sep 13 2023 *)
%t A167919 coxG[{16,66,-11}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Mar 28 2018 *)
%o A167919 (Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+x)*(1-x^16)/(1-12*x+77*x^16-66*x^17) )); // _G. C. Greubel_, Sep 13 2023
%o A167919 (SageMath)
%o A167919 def A167919_list(prec):
%o A167919 P.<x> = PowerSeriesRing(ZZ, prec)
%o A167919 return P( (1+x)*(1-x^16)/(1-12*x+77*x^16-66*x^17) ).list()
%o A167919 A167919_list(40) # _G. C. Greubel_, Sep 13 2023
%Y A167919 Cf. A154638, A169452, A170732.
%Y A167919 Cf. A167881, A167882, A167896 - A167900, A167908, A167914, A167916, A167922, A167923, A167924, A167926, A167927, A167929, A167931, A167933, A167935, A167937, A167938, A167940 - A167947, A167949 - A167962, A167978, A167980, A167988, A167989.
%K A167919 nonn
%O A167919 0,2
%A A167919 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009