cp's OEIS Frontend

A170399 Number of reduced words of length n in Coxeter group on 6 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.

%I A170399 #9 Nov 21 2016 17:17:00
%S A170399 1,6,30,150,750,3750,18750,93750,468750,2343750,11718750,58593750,
%T A170399 292968750,1464843750,7324218750,36621093750,183105468750,
%U A170399 915527343750,4577636718750,22888183593750,114440917968750,572204589843750
%N A170399 Number of reduced words of length n in Coxeter group on 6 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.
%C A170399 The initial terms coincide with those of A003948, although the two sequences are eventually different.
%C A170399 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170399 <a href="/index/Rec#order_44">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, 4, 4, 4, 4, 4, 4, 4, -10).
%F A170399 G.f. (t^44 + 2*t^43 + 2*t^42 + 2*t^41 + 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 +
%F A170399 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 +
%F A170399 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 +
%F A170399 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 +
%F A170399 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
%F A170399 + 2*t^3 + 2*t^2 + 2*t + 1)/(10*t^44 - 4*t^43 - 4*t^42 - 4*t^41 - 4*t^40
%F A170399 - 4*t^39 - 4*t^38 - 4*t^37 - 4*t^36 - 4*t^35 - 4*t^34 - 4*t^33 - 4*t^32
%F A170399 - 4*t^31 - 4*t^30 - 4*t^29 - 4*t^28 - 4*t^27 - 4*t^26 - 4*t^25 - 4*t^24
%F A170399 - 4*t^23 - 4*t^22 - 4*t^21 - 4*t^20 - 4*t^19 - 4*t^18 - 4*t^17 - 4*t^16
%F A170399 - 4*t^15 - 4*t^14 - 4*t^13 - 4*t^12 - 4*t^11 - 4*t^10 - 4*t^9 - 4*t^8 -
%F A170399 4*t^7 - 4*t^6 - 4*t^5 - 4*t^4 - 4*t^3 - 4*t^2 - 4*t + 1)
%t A170399 With[{num=Total[2t^Range[43]]+t^44+1,den=Total[-4 t^Range[43]]+10t^44+1}, CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Mar 02 2012 *)
%K A170399 nonn
%O A170399 0,2
%A A170399 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009