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A170673 Number of reduced words of length n in Coxeter group on 40 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.

%I A170673 #12 Nov 21 2016 11:32:58
%S A170673 1,40,1560,60840,2372760,92537640,3608967960,140749750440,
%T A170673 5489240267160,214080370419240,8349134446350360,325616243407664040,
%U A170673 12699033492898897560,495262306223057004840,19315229942699223188760
%N A170673 Number of reduced words of length n in Coxeter group on 40 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.
%C A170673 The initial terms coincide with those of A170759, although the two sequences are eventually different.
%C A170673 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170673 Vincenzo Librandi, <a href="/A170673/b170673.txt">Table of n, a(n) for n = 0..200</a>
%H A170673 <a href="/index/Rec#order_49">Index entries for linear recurrences with constant coefficients</a>, signature (38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, -741).
%F A170673 G.f. (t^49 + 2*t^48 + 2*t^47 + 2*t^46 + 2*t^45 + 2*t^44 + 2*t^43 + 2*t^42 +
%F A170673 2*t^41 + 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 +
%F A170673 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 +
%F A170673 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 +
%F A170673 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 +
%F A170673 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t +
%F A170673 1)/(741*t^49 - 38*t^48 - 38*t^47 - 38*t^46 - 38*t^45 - 38*t^44 - 38*t^43
%F A170673 - 38*t^42 - 38*t^41 - 38*t^40 - 38*t^39 - 38*t^38 - 38*t^37 - 38*t^36 -
%F A170673 38*t^35 - 38*t^34 - 38*t^33 - 38*t^32 - 38*t^31 - 38*t^30 - 38*t^29 -
%F A170673 38*t^28 - 38*t^27 - 38*t^26 - 38*t^25 - 38*t^24 - 38*t^23 - 38*t^22 -
%F A170673 38*t^21 - 38*t^20 - 38*t^19 - 38*t^18 - 38*t^17 - 38*t^16 - 38*t^15 -
%F A170673 38*t^14 - 38*t^13 - 38*t^12 - 38*t^11 - 38*t^10 - 38*t^9 - 38*t^8 -
%F A170673 38*t^7 - 38*t^6 - 38*t^5 - 38*t^4 - 38*t^3 - 38*t^2 - 38*t + 1)
%t A170673 With[{num=Total[2t^Range[48]]+t^49+1,den=Total[-38 t^Range[48]]+741t^49+ 1},CoefficientList[Series[num/den,{t,0,20}],t]] (* _Harvey P. Dale_, Jul 21 2014 *)
%K A170673 nonn
%O A170673 0,2
%A A170673 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009