

A156945


Growth sequence for Richard Thompson's group F with the standard generating set x_0, x_1.


2



1, 4, 12, 36, 108, 314, 906, 2576, 7280, 20352, 56664, 156570, 431238, 1180968, 3225940, 8773036, 23809148, 64388402, 173829458, 467950860, 1257901236, 3373450744, 9035758992
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OFFSET

0,2


COMMENTS

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}.


REFERENCES

M. Elder, E. Fusy, A. Rechnitzer, Counting elements and geodesics in Thompson's Group F, J. Alg. 324 (2010) 102121 doi:10.1016/j.jalgebra.2010.02.035


LINKS

Murray Elder, Table of n, a(n) for n = 0..1500
J. Burillo, S. Cleary and B. Wiest, Computational explorations in Thompson's group F In Geometric Group Theory, Geneva and Barcelona Conferences, Birkhauser, 2007.
M. Elder, É. Fusy and A. Rechnitzer, Counting elements and geodesics in Thompson's group F, arXiv:0902.0202 [math.GR]
V. S. Guba, On the Properties of the Cayley Graph of Richard Thompson's Group F, arXiv:math/0211396 [math.GR]
V. S. Guba, On the Properties of the Cayley Graph of Richard Thompson's Group F, Int. J. of Alg. Computation, 14(56):677702, 2004.


EXAMPLE

For n=1 there are a(1)=4 elements: x_0, x_0^{1}, x_1, x_1^{1}.


CROSSREFS

Sequence in context: A199937 A290380 A003212 * A006817 A163315 A003119
Adjacent sequences: A156942 A156943 A156944 * A156946 A156947 A156948


KEYWORD

nonn


AUTHOR

Murray Elder, Feb 19 2009


STATUS

approved



