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A170390 Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.

%I A170390 #8 Nov 21 2016 19:37:10
%S A170390 1,45,1980,87120,3833280,168664320,7421230080,326534123520,
%T A170390 14367501434880,632170063134720,27815482777927680,1223881242228817920,
%U A170390 53850774658067988480,2369434084954991493120,104255099738019625697280
%N A170390 Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.
%C A170390 The initial terms coincide with those of A170764, although the two sequences are eventually different.
%C A170390 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170390 <a href="/index/Rec#order_43">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, 43, 43, 43, 43, 43, -946).
%F A170390 G.f. (t^43 + 2*t^42 + 2*t^41 + 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 +
%F A170390 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 +
%F A170390 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 +
%F A170390 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 +
%F A170390 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3
%F A170390 + 2*t^2 + 2*t + 1)/(946*t^43 - 43*t^42 - 43*t^41 - 43*t^40 - 43*t^39 -
%F A170390 43*t^38 - 43*t^37 - 43*t^36 - 43*t^35 - 43*t^34 - 43*t^33 - 43*t^32 -
%F A170390 43*t^31 - 43*t^30 - 43*t^29 - 43*t^28 - 43*t^27 - 43*t^26 - 43*t^25 -
%F A170390 43*t^24 - 43*t^23 - 43*t^22 - 43*t^21 - 43*t^20 - 43*t^19 - 43*t^18 -
%F A170390 43*t^17 - 43*t^16 - 43*t^15 - 43*t^14 - 43*t^13 - 43*t^12 - 43*t^11 -
%F A170390 43*t^10 - 43*t^9 - 43*t^8 - 43*t^7 - 43*t^6 - 43*t^5 - 43*t^4 - 43*t^3 -
%F A170390 43*t^2 - 43*t + 1)
%t A170390 With[{num=Total[2t^Range[42]]+t^43+1,den=Total[-43 t^Range[42]]+946t^43+ 1},CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Mar 19 2013 *)
%K A170390 nonn
%O A170390 0,2
%A A170390 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009