A166877 - OEIS

%I #13 Nov 24 2016 10:23:43

%S 1,6,30,150,750,3750,18750,93750,468750,2343750,11718750,58593750,

%T 292968750,1464843735,7324218600,36621092640,183105461400,

%U 915527298000,4577636445000,22888182000000,114440908875000,572204538750000

%N Number of reduced words of length n in Coxeter group on 6 generators S_i with relations (S_i)^2 = (S_i S_j)^13 = I.

%C The initial terms coincide with those of A003948, 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="/A166877/b166877.txt">Table of n, a(n) for n = 0..500</a>

%H <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, -10).

%F 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)/(10*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 With[{num=Total[2t^Range[12]]+t^13+1,den=Total[-4 t^Range[12]]+ 10t^13+ 1}, CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Jul 27 2011 *)

%t 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)/(10*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_, May 27 2016 *)

%K nonn

%O 0,2

%A _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009