cp's OEIS Frontend

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.

A167100 Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^13 = I.

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%I A167100 #12 Aug 07 2021 13:56:36
%S A167100 1,47,2162,99452,4574792,210440432,9680259872,445291954112,
%T A167100 20483429889152,942237774900992,43342937645445632,1993775131690499072,
%U A167100 91713656057762957312,4218828178657096035271,194066096218226417572740
%N A167100 Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^13 = I.
%C A167100 The initial terms coincide with those of A170766, although the two sequences are eventually different.
%C A167100 Computed with MAGMA using commands similar to those used to compute A154638.
%H A167100 G. C. Greubel, <a href="/A167100/b167100.txt">Table of n, a(n) for n = 0..500</a>
%H A167100 <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, -1035).
%F A167100 G.f.: (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)/(1035*t^13 - 45*t^12 - 45*t^11 - 45*t^10 - 45*t^9 - 45*t^8 - 45*t^7 - 45*t^6 - 45*t^5 - 45*t^4 - 45*t^3 - 45*t^2 - 45*t + 1).
%t A167100 CoefficientList[Series[(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)/(1035*t^13 - 45*t^12 - 45*t^11 - 45*t^10 - 45*t^9 - 45*t^8 - 45*t^7 - 45*t^6 - 45*t^5 - 45*t^4 - 45*t^3 - 45*t^2 - 45*t + 1), {t, 0, 50}], t] (* _G. C. Greubel_, Jun 02 2016 *)
%t A167100 coxG[{13,1035,-45}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Aug 07 2021 *)
%K A167100 nonn
%O A167100 0,2
%A A167100 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009