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%I #13 Jun 15 2018 10:34:18
%S 1,4,12,36,108,324,952,2800,8132,23608,67884,195132,556932,1588836,
%T 4507524,12782560,36088224,101845032,286372148,804930196,2255624360,
%U 6318588308,17654567968
%N Geodesic growth sequence for Richard Thompson's group F with the standard generating set x_0, x_1.
%C a(n) is the number of geodesics of length n in the Cayley graph of Richard Thompson's group F with the standard generating set {x_0, x_1}.
%D M. Elder, E. Fusy, A. Rechnitzer, Counting elements and geodesics in Thompson's Group F, J. Alg. 324 (2010) 102-121 doi:10.1016/j.jalgebra.2010.02.035
%H M. Elder, É. Fusy and A. Rechnitzer, <a href="http://arxiv.org/abs/0902.0202">Counting elements and geodesics in Thompson's group F</a>, arxiv:0902.0202
%H R. Grigorchuk and T. Smirnova-Nagnibeda, <a href="http://dx.doi.org/10.1007/s002220050181">Complete growth functions of hyperbolic groups</a>, Inven. Math. 130(1):159--188, 1997.
%e For n=6 there are a(6)=952 geodesics of length 6: there are 4 * 3^5 = 972 reduced words in the letters x_0, x_0^{-1}, x_1, x_1^{-1}, and the shortest relation in F has length 10.
%Y Cf. A156945, the number of elements in F.
%K nonn
%O 0,2
%A _Murray Elder_, Feb 19 2009