cp's OEIS Frontend

A170091 Number of reduced words of length n in Coxeter group on 34 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.

%I A170091 #9 Nov 26 2016 10:06:53
%S A170091 1,34,1122,37026,1221858,40321314,1330603362,43909910946,
%T A170091 1449027061218,47817893020194,1577990469666402,52073685498991266,
%U A170091 1718431621466711778,56708243508401488674,1871372035777249126242,61755277180649221165986
%N A170091 Number of reduced words of length n in Coxeter group on 34 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.
%C A170091 The initial terms coincide with those of A170753, although the two sequences are eventually different.
%C A170091 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170091 <a href="/index/Rec#order_37">Index entries for linear recurrences with constant coefficients</a>, signature (32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, -528).
%F A170091 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 A170091 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 A170091 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 A170091 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 A170091 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(528*t^37 - 32*t^36 - 32*t^35 -
%F A170091 32*t^34 - 32*t^33 - 32*t^32 - 32*t^31 - 32*t^30 - 32*t^29 - 32*t^28 -
%F A170091 32*t^27 - 32*t^26 - 32*t^25 - 32*t^24 - 32*t^23 - 32*t^22 - 32*t^21 -
%F A170091 32*t^20 - 32*t^19 - 32*t^18 - 32*t^17 - 32*t^16 - 32*t^15 - 32*t^14 -
%F A170091 32*t^13 - 32*t^12 - 32*t^11 - 32*t^10 - 32*t^9 - 32*t^8 - 32*t^7 -
%F A170091 32*t^6 - 32*t^5 - 32*t^4 - 32*t^3 - 32*t^2 - 32*t + 1)
%t A170091 With[{num=Total[2t^Range[36]]+t^37+1,den=Total[-32 t^Range[36]]+ 528t^37+ 1}, CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Oct 26 2011 *)
%K A170091 nonn
%O A170091 0,2
%A A170091 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009