

A156946


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


0



1, 4, 12, 36, 108, 324, 952, 2800, 8132, 23608, 67884, 195132, 556932, 1588836, 4507524, 12782560, 36088224, 101845032, 286372148, 804930196, 2255624360, 6318588308, 17654567968
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OFFSET

0,2


COMMENTS

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}.


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

Table of n, a(n) for n=0..22.
M. Elder, É. Fusy and A. Rechnitzer, Counting elements and geodesics in Thompson's group F, arxiv:0902.0202
R. Grigorchuk and T. SmirnovaNagnibeda, Complete growth functions of hyperbolic groups, Inven. Math. 130(1):159188, 1997.


EXAMPLE

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.


CROSSREFS

Cf. A156945, the number of elements in F.
Sequence in context: A326339 A003119 A001394 * A163877 A164353 A164697
Adjacent sequences: A156943 A156944 A156945 * A156947 A156948 A156949


KEYWORD

nonn


AUTHOR

Murray Elder, Feb 19 2009


STATUS

approved



