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A170726 Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.

%I A170726 #12 Nov 18 2016 17:38:47
%S A170726 1,45,1980,87120,3833280,168664320,7421230080,326534123520,
%T A170726 14367501434880,632170063134720,27815482777927680,1223881242228817920,
%U A170726 53850774658067988480,2369434084954991493120,104255099738019625697280
%N A170726 Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.
%C A170726 The initial terms coincide with those of A170764, although the two sequences are eventually different.
%C A170726 Computed with MAGMA using commands similar to those used to compute A154638.
%C A170726 About the initial comment, first disagreement is at index 50 and the difference is 990.  - _Vincenzo Librandi_, Dec 08 2012
%H A170726 Vincenzo Librandi, <a href="/A170726/b170726.txt">Table of n, a(n) for n = 0..200</a>
%H A170726 <a href="/index/Rec#order_50">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, 43, 43, 43, 43, 43, 43, 43, -946).
%F A170726 G.f. (t^50 + 2*t^49 + 2*t^48 + 2*t^47 + 2*t^46 + 2*t^45 + 2*t^44 + 2*t^43 +
%F A170726 2*t^42 + 2*t^41 + 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 +
%F A170726 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 +
%F A170726 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 +
%F A170726 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 +
%F A170726 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 +
%F A170726 2*t + 1)/(946*t^50 - 43*t^49 - 43*t^48 - 43*t^47 - 43*t^46 - 43*t^45 -
%F A170726 43*t^44 - 43*t^43 - 43*t^42 - 43*t^41 - 43*t^40 - 43*t^39 - 43*t^38 -
%F A170726 43*t^37 - 43*t^36 - 43*t^35 - 43*t^34 - 43*t^33 - 43*t^32 - 43*t^31 -
%F A170726 43*t^30 - 43*t^29 - 43*t^28 - 43*t^27 - 43*t^26 - 43*t^25 - 43*t^24 -
%F A170726 43*t^23 - 43*t^22 - 43*t^21 - 43*t^20 - 43*t^19 - 43*t^18 - 43*t^17 -
%F A170726 43*t^16 - 43*t^15 - 43*t^14 - 43*t^13 - 43*t^12 - 43*t^11 - 43*t^10 -
%F A170726 43*t^9 - 43*t^8 - 43*t^7 - 43*t^6 - 43*t^5 - 43*t^4 - 43*t^3 - 43*t^2 -
%F A170726 43*t + 1)
%t A170726 With[{num=Total[2t^Range[49]]+t^50+1,den=Total[-43 t^Range[49]]+ 946t^50+1}, CoefficientList[Series[num/den,{t,0,20}],t]] (* _Harvey P. Dale_, Oct 20 2011 *)
%K A170726 nonn
%O A170726 0,2
%A A170726 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009