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 A167908 #19 Jul 23 2024 18:49:37
%S A167908 1,10,90,810,7290,65610,590490,5314410,47829690,430467210,3874204890,
%T A167908 34867844010,313810596090,2824295364810,25418658283290,
%U A167908 228767924549610,2058911320946445,18530201888517600,166771816996654800
%N A167908 Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^16 = I.
%C A167908 The initial terms coincide with those of A003952, although the two sequences are eventually different.
%C A167908 Computed with MAGMA using commands similar to those used to compute A154638.
%H A167908 G. C. Greubel, <a href="/A167908/b167908.txt">Table of n, a(n) for n = 0..500</a>
%H A167908 <a href="/index/Rec#order_16">Index entries for linear recurrences with constant coefficients</a>, signature (8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,-36).
%F A167908 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)/( 36*t^16 - 8*t^15 - 8*t^14 - 8*t^13 - 8*t^12 - 8*t^11 - 8*t^10 - 8*t^9 - 8*t^8 - 8*t^7 - 8*t^6 - 8*t^5 - 8*t^4 - 8*t^3 - 8*t^2 - 8*t + 1).
%F A167908 From _G. C. Greubel_, Jul 23 2024: (Start)
%F A167908 a(n) = 8*Sum_{j=1..15} a(n-j) - 36*a(n-16).
%F A167908 G.f.: (1+t)*(1 - t^16)/(1 - 9*t + 44*t^16 - 36*t^17). (End)
%t A167908 With[{a=36, b=8}, CoefficientList[Series[(1+t)*(1-t^16)/(1-(b+1)*t +(a + b)*t^16 -a*t^17), {t,0,40}], t]] (* _G. C. Greubel_, Jul 01 2016; Jul 23 2024 *)
%t A167908 coxG[{16,36,-8}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jun 04 2017 *)
%o A167908 (Magma)
%o A167908 R<x>:=PowerSeriesRing(Integers(), 30);
%o A167908 Coefficients(R!( (1+x)*(1-x^16)/(1-9*x+44*x^16-36*x^17) )); // _G. C. Greubel_, Jul 23 2024
%o A167908 (SageMath)
%o A167908 def A167908_list(prec):
%o A167908 P.<x> = PowerSeriesRing(ZZ, prec)
%o A167908 return P( (1+x)*(1-x^16)/(1-9*x+44*x^16-36*x^17) ).list()
%o A167908 A167908_list(30) # _G. C. Greubel_, Jul 23 2024
%Y A167908 Cf. A003952, A154638, A169452.
%K A167908 nonn
%O A167908 0,2
%A A167908 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009