A156945 Growth sequence for Richard Thompson's group F with the standard generating set x_0, x_1.

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

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) 102-121 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(5-6):677-702, 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 A326339

Adjacent sequences: A156942 A156943 A156944 * A156946 A156947 A156948

Keyword

nonn

Author

Murray Elder, Feb 19 2009

Status

approved