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 A167914 #14 Dec 04 2024 05:51:01
%S A167914 1,11,110,1100,11000,110000,1100000,11000000,110000000,1100000000,
%T A167914 11000000000,110000000000,1100000000000,11000000000000,
%U A167914 110000000000000,1100000000000000,10999999999999945,109999999999998900
%N A167914 Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^16 = I.
%C A167914 The initial terms coincide with those of A003953, although the two sequences are eventually different.
%C A167914 Computed with MAGMA using commands similar to those used to compute A154638.
%H A167914 G. C. Greubel, <a href="/A167914/b167914.txt">Table of n, a(n) for n = 0..500</a>
%H A167914 <a href="/index/Rec#order_16">Index entries for linear recurrences with constant coefficients</a>, signature (9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,-45).
%F A167914 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)/( 45*t^16 - 9*t^15 - 9*t^14 - 9*t^13 - 9*t^12 - 9*t^11 - 9*t^10 - 9*t^9 - 9*t^8 - 9*t^7 - 9*t^6 - 9*t^5 - 9*t^4 - 9*t^3 - 9*t^2 - 9*t + 1).
%F A167914 From _G. C. Greubel_, Dec 04 2024: (Start)
%F A167914 a(n) = 9*Sum_{j=1..15} a(n-j) - 45*a(n-16).
%F A167914 G.f.: (1+x)*(1-x^16)/(1 - 10*x + 54*x^16 - 45*x^17). (End)
%t A167914 CoefficientList[Series[(1+t)*(1-t^16)/(1-10*t+54*t^16-45*t^17), {t,0,50}], t] (* _G. C. Greubel_, Jul 01 2016; Dec 04 2024 *)
%t A167914 coxG[{16,45,-9}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, Dec 04 2024 *)
%o A167914 (Magma)
%o A167914 R<x>:=PowerSeriesRing(Integers(), 40);
%o A167914 Coefficients(R!( (1+x)*(1-x^16)/(1-10*x+54*x^16-45*x^17) )); // _G. C. Greubel_, Dec 04 2024
%o A167914 (SageMath)
%o A167914 def A167914_list(prec):
%o A167914 P.<x> = PowerSeriesRing(ZZ, prec)
%o A167914 return P( (1+x)*(1-x^16)/(1-10*x+54*x^16-45*x^17) ).list()
%o A167914 A167914_list(40) # _G. C. Greubel_, Dec 04 2024
%Y A167914 Cf. A003953, A154638, A169452.
%K A167914 nonn
%O A167914 0,2
%A A167914 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009