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 A167882 #14 Dec 07 2024 01:59:25
%S A167882 1,4,12,36,108,324,972,2916,8748,26244,78732,236196,708588,2125764,
%T A167882 6377292,19131876,57395622,172186848,516560496,1549681344,4649043600,
%U A167882 13947129504,41841384624,125524142208,376572391632,1129717069920
%N A167882 Number of reduced words of length n in Coxeter group on 4 generators S_i with relations (S_i)^2 = (S_i S_j)^16 = I.
%C A167882 The initial terms coincide with those of A003946, although the two sequences are eventually different.
%C A167882 Computed with MAGMA using commands similar to those used to compute A154638.
%H A167882 G. C. Greubel, <a href="/A167882/b167882.txt">Table of n, a(n) for n = 0..500</a>
%H A167882 <a href="/index/Rec#order_16">Index entries for linear recurrences with constant coefficients</a>, signature (2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,-3).
%F A167882 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) / ( 3*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).
%F A167882 From _G. C. Greubel_, Jan 17 2023: (Start)
%F A167882 a(n) = 2*Sum_{j=1..15} a(n-j) - 3*a(n-16).
%F A167882 G.f.: (1+x)*(1-x^16)/(1 - 3*x + 5*x^16 - 3*x^17). (End)
%t A167882 CoefficientList[Series[(1+t)*(1-t^16)/(1-3*t+5*t^16-3*t^17), {t,0,50}], t] (* _G. C. Greubel_, Jun 29 2016; Dec 06 2024 *)
%t A167882 coxG[{16,3,-2}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, Dec 06 2024 *)
%o A167882 (Magma)
%o A167882 R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+x)*(1-x^16)/(1-3*x+5*x^16-3*x^17) )); // _G. C. Greubel_, Dec 06 2024
%o A167882 (SageMath)
%o A167882 def A167882_list(prec):
%o A167882 P.<x> = PowerSeriesRing(ZZ, prec)
%o A167882 return P( (1+x)*(1-x^16)/(1-3*x+5*x^16-3*x^17) ).list()
%o A167882 print(A167882_list(40)) # _G. C. Greubel_, Dec 06 2024
%Y A167882 Cf. A003946, A154638, A169452.
%K A167882 nonn
%O A167882 0,2
%A A167882 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009