cp's OEIS Frontend

A170150 Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^38 = I.

%I A170150 #8 May 14 2017 17:42:48
%S A170150 1,45,1980,87120,3833280,168664320,7421230080,326534123520,
%T A170150 14367501434880,632170063134720,27815482777927680,1223881242228817920,
%U A170150 53850774658067988480,2369434084954991493120,104255099738019625697280
%N A170150 Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^38 = I.
%C A170150 The initial terms coincide with those of A170764, although the two sequences are eventually different.
%C A170150 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170150 <a href="/index/Rec#order_38">Index entries for linear recurrences with constant coefficients</a>, signature (43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, -946).
%F A170150 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 A170150 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 A170150 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 A170150 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 A170150 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(946*t^38 - 43*t^37 -
%F A170150 43*t^36 - 43*t^35 - 43*t^34 - 43*t^33 - 43*t^32 - 43*t^31 - 43*t^30 -
%F A170150 43*t^29 - 43*t^28 - 43*t^27 - 43*t^26 - 43*t^25 - 43*t^24 - 43*t^23 -
%F A170150 43*t^22 - 43*t^21 - 43*t^20 - 43*t^19 - 43*t^18 - 43*t^17 - 43*t^16 -
%F A170150 43*t^15 - 43*t^14 - 43*t^13 - 43*t^12 - 43*t^11 - 43*t^10 - 43*t^9 -
%F A170150 43*t^8 - 43*t^7 - 43*t^6 - 43*t^5 - 43*t^4 - 43*t^3 - 43*t^2 - 43*t + 1)
%t A170150 With[{num=Total[2t^Range[37]]+t^38+1,den=Total[-43 t^Range[37]]+946t^38+ 1},CoefficientList[Series[num/den,{t,0,20}],t]] (* _Harvey P. Dale_, Dec 09 2013 *)
%K A170150 nonn
%O A170150 0,2
%A A170150 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009