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%I #19 Jun 15 2018 10:33:51
%S 1,4,12,36,108,314,906,2576,7280,20352,56664,156570,431238,1180968,
%T 3225940,8773036,23809148,64388402,173829458,467950860,1257901236,
%U 3373450744,9035758992
%N Growth sequence for Richard Thompson's group F with the standard generating set x_0, x_1.
%C a(n) is the number of elements in the sphere of radius 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 Murray Elder, <a href="/A156945/b156945.txt">Table of n, a(n) for n = 0..1500</a>
%H J. Burillo, S. Cleary and B. Wiest, <a href="http://dx.doi.org/10.1007/978-3-7643-8412-8_2">Computational explorations in Thompson's group F</a> In Geometric Group Theory, Geneva and Barcelona Conferences, Birkhauser, 2007.
%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 [math.GR]
%H V. S. Guba, <a href="http://arxiv.org/abs/math/0211396">On the Properties of the Cayley Graph of Richard Thompson's Group F</a>, arXiv:math/0211396 [math.GR]
%H V. S. Guba, <a href="http://dx.doi.org/10.1142/S021819670400192X">On the Properties of the Cayley Graph of Richard Thompson's Group F</a>, Int. J. of Alg. Computation, 14(5-6):677-702, 2004.
%e For n=1 there are a(1)=4 elements: x_0, x_0^{-1}, x_1, x_1^{-1}.
%K nonn
%O 0,2
%A _Murray Elder_, Feb 19 2009
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