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%I #10 Nov 24 2016 10:25:40
%S 1,12,132,1452,15972,175692,1932612,21258732,233846052,2572306572,
%T 28295372292,311249095212,3423740047332,37661140520586,
%U 414272545725720,4556998002975000,50126978032637880,551396758358058360
%N Number of reduced words of length n in Coxeter group on 12 generators S_i with relations (S_i)^2 = (S_i S_j)^13 = I.
%C The initial terms coincide with those of A003954, 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="/A166951/b166951.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 (10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, -55).
%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)/(55*t^13 - 10*t^12 - 10*t^11 - 10*t^10 - 10*t^9 - 10*t^8 - 10*t^7 - 10*t^6 - 10*t^5 - 10*t^4 - 10*t^3 - 10*t^2 - 10*t + 1).
%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)/(55*t^13 - 10*t^12 - 10*t^11 - 10*t^10 - 10*t^9 - 10*t^8 - 10*t^7 - 10*t^6 - 10*t^5 - 10*t^4 - 10*t^3 - 10*t^2 - 10*t + 1), {t, 0, 50}], t] (* _G. C. Greubel_, May 29 2016 *)
%K nonn
%O 0,2
%A _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009
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