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.

A167107 Number of reduced words of length n in Coxeter group on 6 generators S_i with relations (S_i)^2 = (S_i S_j)^14 = I.

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%I A167107 #9 Nov 24 2016 10:43:09
%S A167107 1,6,30,150,750,3750,18750,93750,468750,2343750,11718750,58593750,
%T A167107 292968750,1464843750,7324218735,36621093600,183105467640,
%U A167107 915527336400,4577636673000,22888183320000,114440916375000,572204580750000
%N A167107 Number of reduced words of length n in Coxeter group on 6 generators S_i with relations (S_i)^2 = (S_i S_j)^14 = I.
%C A167107 The initial terms coincide with those of A003948, although the two sequences are eventually different.
%C A167107 Computed with MAGMA using commands similar to those used to compute A154638.
%H A167107 G. C. Greubel, <a href="/A167107/b167107.txt">Table of n, a(n) for n = 0..500</a>
%H A167107 <a href="/index/Rec#order_14">Index entries for linear recurrences with constant coefficients</a>, signature (4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, -10).
%F A167107 G.f.: (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)/(10*t^14 - 4*t^13 - 4*t^12 - 4*t^11 - 4*t^10 - 4*t^9 - 4*t^8 - 4*t^7 - 4*t^6 - 4*t^5 - 4*t^4 - 4*t^3 - 4*t^2 - 4*t + 1).
%t A167107 CoefficientList[Series[(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)/ (10*t^14 - 4*t^13 - 4*t^12 - 4*t^11 - 4*t^10 - 4*t^9 - 4*t^8 - 4*t^7 - 4*t^6 - 4*t^5 - 4*t^4 - 4*t^3 - 4*t^2 - 4*t + 1), {t, 0, 50}], t] (* _G. C. Greubel_, Jun 03 2016 *)
%K A167107 nonn
%O A167107 0,2
%A A167107 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009