A156946 Geodesic growth sequence for Richard Thompson's group F with the standard generating set x_0, x_1.

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

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) 102-121 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. Smirnova-Nagnibeda, Complete growth functions of hyperbolic groups, Inven. Math. 130(1):159--188, 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: A334877 A003119 A001394 * A163877 A336262 A164353

Adjacent sequences: A156943 A156944 A156945 * A156947 A156948 A156949

Keyword

nonn

Author

Murray Elder, Feb 19 2009

Status

approved