cp's OEIS Frontend

A170063 Number of reduced words of length n in Coxeter group on 6 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.

%I A170063 #9 Nov 26 2016 09:59:18
%S A170063 1,6,30,150,750,3750,18750,93750,468750,2343750,11718750,58593750,
%T A170063 292968750,1464843750,7324218750,36621093750,183105468750,
%U A170063 915527343750,4577636718750,22888183593750,114440917968750,572204589843750
%N A170063 Number of reduced words of length n in Coxeter group on 6 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.
%C A170063 The initial terms coincide with those of A003948, although the two sequences are eventually different.
%C A170063 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170063 <a href="/index/Rec#order_37">Index entries for linear recurrences with constant coefficients</a>, signature (4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, -10).
%F A170063 G.f. (t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 +
%F A170063 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 +
%F A170063 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 +
%F A170063 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 +
%F A170063 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(10*t^37 - 4*t^36 - 4*t^35 -
%F A170063 4*t^34 - 4*t^33 - 4*t^32 - 4*t^31 - 4*t^30 - 4*t^29 - 4*t^28 - 4*t^27 -
%F A170063 4*t^26 - 4*t^25 - 4*t^24 - 4*t^23 - 4*t^22 - 4*t^21 - 4*t^20 - 4*t^19 -
%F A170063 4*t^18 - 4*t^17 - 4*t^16 - 4*t^15 - 4*t^14 - 4*t^13 - 4*t^12 - 4*t^11 -
%F A170063 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 -
%F A170063 4*t + 1)
%t A170063 With[{num=Total[2t^Range[36]]+t^37+1,den=Total[-4 t^Range[36]]+ 10t^37+ 1},CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Oct 26 2011 *)
%K A170063 nonn
%O A170063 0,2
%A A170063 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009