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 A167980 #16 Jan 17 2023 07:17:26
%S A167980 1,48,2256,106032,4983504,234224688,11008560336,517402335792,
%T A167980 24317909782224,1142941759764528,53718262708932816,
%U A167980 2524758347319842352,118663642324032590544,5577191189229531755568,262127985893787992511696
%N A167980 Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^16 = I.
%C A167980 The initial terms coincide with those of A170767, although the two sequences are eventually different.
%C A167980 Computed with MAGMA using commands similar to those used to compute A154638.
%H A167980 G. C. Greubel, <a href="/A167980/b167980.txt">Table of n, a(n) for n = 0..500</a>
%H A167980 <a href="/index/Rec#order_16">Index entries for linear recurrences with constant coefficients</a>, signature (46,46,46,46,46,46,46,46,46,46,46,46,46,46,46,-1081).
%F A167980 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)/( 1081*t^16 - 46*t^15 - 46*t^14 - 46*t^13 - 46*t^12 - 46*t^11 - 46*t^10 - 46*t^9 - 46*t^8 - 46*t^7 - 46*t^6 - 46*t^5 - 46*t^4 - 46*t^3 - 46*t^2 - 46*t + 1).
%F A167980 From _G. C. Greubel_, Jan 17 2023: (Start)
%F A167980 a(n) = Sum_{j=1..15} a(n-j) - 1081*a(n-16).
%F A167980 G.f.: (1+x)*(1-x^17)/(1 - 47*x + 1127*x^16 - 1081*x^17). (End)
%t A167980 coxG[{16,1081,-46}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jun 12 2016 *)
%t A167980 CoefficientList[Series[(1+t)*(1-t^17)/(1-47*t+1127*t^16-1081*t^17), {t, 0,50}], t] (* _G. C. Greubel_, Jul 03 2016; Jan 17 2023 *)
%o A167980 (Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+x)*(1-x^17)/(1-47*x+1127*x^16-1081*x^17) )); // _G. C. Greubel_, Jan 17 2023
%o A167980 (SageMath)
%o A167980 def A167980_list(prec):
%o A167980 P.<x> = PowerSeriesRing(ZZ, prec)
%o A167980 return P( (1+x)*(1-x^17)/(1-47*x+1127*x^16-1081*x^17) ).list()
%o A167980 A167980_list(30) # _G. C. Greubel_, Jan 17 2023
%Y A167980 Cf. A154638, A169452, A170767.
%K A167980 nonn
%O A167980 0,2
%A A167980 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009