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%I #11 Nov 24 2016 10:37:55
%S 1,50,2450,120050,5882450,288240050,14123762450,692064360050,
%T 33911153642450,1661646528480050,81420679895522450,
%U 3989613314880600050,195491052429149402450,9579061569028320718825,469374016882387715162400
%N Number of reduced words of length n in Coxeter group on 50 generators S_i with relations (S_i)^2 = (S_i S_j)^13 = I.
%C The initial terms coincide with those of A170769, although the two sequences are eventually different.
%C Computed with MAGMA using commands similar to those used to compute A154638.
%H G. C. Greubel, <a href="/A167103/b167103.txt">Table of n, a(n) for n = 0..500</a>
%H <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, -1176).
%F G.f.: (t^13 + 2*t^12 + 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 + 2*t^2 + 2*t + 1)/(1176*t^13 - 48*t^12 - 48*t^11 - 48*t^10 - 48*t^9 - 48*t^8 - 48*t^7 - 48*t^6 - 48*t^5 - 48*t^4 - 48*t^3 - 48*t^2 - 48*t + 1).
%t coxG[{13,1176,-48}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Apr 12 2015 *)
%t CoefficientList[Series[(t^13 + 2*t^12 + 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 + 2*t^2 + 2*t + 1)/(1176*t^13 - 48*t^12 - 48*t^11 - 48*t^10 - 48*t^9 - 48*t^8 - 48*t^7 - 48*t^6 - 48*t^5 - 48*t^4 - 48*t^3 - 48*t^2 - 48*t + 1), {t, 0, 50}], t] (* _G. C. Greubel_, Jun 03 2016 *)
%K nonn
%O 0,2
%A _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009
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