cp's OEIS Frontend

A170139 Number of reduced words of length n in Coxeter group on 34 generators S_i with relations (S_i)^2 = (S_i S_j)^38 = I.

%I A170139 #8 May 14 2017 17:37:51
%S A170139 1,34,1122,37026,1221858,40321314,1330603362,43909910946,
%T A170139 1449027061218,47817893020194,1577990469666402,52073685498991266,
%U A170139 1718431621466711778,56708243508401488674,1871372035777249126242,61755277180649221165986
%N A170139 Number of reduced words of length n in Coxeter group on 34 generators S_i with relations (S_i)^2 = (S_i S_j)^38 = I.
%C A170139 The initial terms coincide with those of A170753, although the two sequences are eventually different.
%C A170139 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170139 <a href="/index/Rec#order_38">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, 32, -528).
%F A170139 G.f. (t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 +
%F A170139 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 +
%F A170139 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 +
%F A170139 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 +
%F A170139 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(528*t^38 - 32*t^37 -
%F A170139 32*t^36 - 32*t^35 - 32*t^34 - 32*t^33 - 32*t^32 - 32*t^31 - 32*t^30 -
%F A170139 32*t^29 - 32*t^28 - 32*t^27 - 32*t^26 - 32*t^25 - 32*t^24 - 32*t^23 -
%F A170139 32*t^22 - 32*t^21 - 32*t^20 - 32*t^19 - 32*t^18 - 32*t^17 - 32*t^16 -
%F A170139 32*t^15 - 32*t^14 - 32*t^13 - 32*t^12 - 32*t^11 - 32*t^10 - 32*t^9 -
%F A170139 32*t^8 - 32*t^7 - 32*t^6 - 32*t^5 - 32*t^4 - 32*t^3 - 32*t^2 - 32*t + 1)
%t A170139 With[{num=Total[2t^Range[37]]+t^38+1,den=Total[-32 t^Range[37]]+465t^38+ 1},CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Oct 20 2012 *)
%K A170139 nonn
%O A170139 0,2
%A A170139 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009