%I #11 Nov 26 2016 16:36:01
%S 1,3,6,12,24,48,96,192,384,768,1536,3072,6144,12288,24573,49140,98271,
%T 196524,393012,785952,1571760,3143232,6285888,12570624,25138944,
%U 50273280,100537344,201056256,402075654,804077601,1608007800,3215720823
%N Number of reduced words of length n in Coxeter group on 3 generators S_i with relations (S_i)^2 = (S_i S_j)^14 = I.
%C The initial terms coincide with those of A003945, although the two sequences are eventually different.
%C Computed with MAGMA using commands similar to those used to compute A154638.
%H G. C. Greubel, <a href="/A167104/b167104.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_14">Index entries for linear recurrences with constant coefficients</a>, signature (1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1).
%F 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)/(t^14 - t^13 - t^12 - t^11 - t^10 - t^9 - t^8 - t^7 - t^6 - t^5 - t^4 - t^3 - t^2 - t + 1).
%t 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)/(t^14 - t^13 - t^12 - t^11 - t^10 - t^9 - t^8 - t^7 - t^6 - t^5 - t^4 - t^3 - t^2 - t + 1),{t,0,50}],t] (* _G. C. Greubel_, Jun 03 2016 *)
%K nonn
%O 0,2
%A _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009