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 A167900 #14 Dec 07 2024 01:59:39
%S A167900 1,9,72,576,4608,36864,294912,2359296,18874368,150994944,1207959552,
%T A167900 9663676416,77309411328,618475290624,4947802324992,39582418599936,
%U A167900 316659348799452,2533274790395328,20266198323160356,162129586585264704
%N A167900 Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^16 = I.
%C A167900 The initial terms coincide with those of A003951, although the two sequences are eventually different.
%C A167900 Computed with MAGMA using commands similar to those used to compute A154638.
%H A167900 G. C. Greubel, <a href="/A167900/b167900.txt">Table of n, a(n) for n = 0..500</a>
%H A167900 <a href="/index/Rec#order_16">Index entries for linear recurrences with constant coefficients</a>, signature (7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,-28).
%F A167900 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)/( 28*t^16 - 7*t^15 - 7*t^14 - 7*t^13 - 7*t^12 - 7*t^11 - 7*t^10 - 7*t^9 - 7*t^8 - 7*t^7 - 7*t^6 - 7*t^5 - 7*t^4 - 7*t^3 - 7*t^2 - 7*t + 1).
%F A167900 From _G. C. Greubel_, Dec 06 2024: (Start)
%F A167900 a(n) = 7*Sum_{j=1..15} a(n-j) - 28*a(n-16).
%F A167900 G.f.: (1+x)*(1-x^16)/(1 - 8*x + 35*x^16 - 28*x^17). (End)
%t A167900 CoefficientList[Series[(1+t)*(1-t^16)/(1-8*t+35*t^16-28*t^17), {t,0,50}], t] (* _G. C. Greubel_, Jul 01 2016; Dec 06 2024 *)
%t A167900 coxG[{16,28,-7}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, Dec 06 2024 *)
%o A167900 (Magma)
%o A167900 R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+x)*(1-x^16)/(1-8*x+35*x^16-28*x^17) )); // _G. C. Greubel_, Dec 06 2024
%o A167900 (SageMath)
%o A167900 def A167900_list(prec):
%o A167900 P.<x> = PowerSeriesRing(ZZ, prec)
%o A167900 return P( (1+x)*(1-x^16)/(1-8*x+35*x^16-28*x^17) ).list()
%o A167900 print(A167900_list(40)) # _G. C. Greubel_, Dec 06 2024
%Y A167900 Cf. A003951, A154638, A169452.
%K A167900 nonn
%O A167900 0,2
%A A167900 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009