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Search: id:A156945
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| A156945 |
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Growth sequence for Richard Thompson's group F with the standard generating set x_0,x_1. |
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+0
2
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| 1, 4, 12, 36, 108, 314, 906, 2576, 7280, 20352, 56664, 156570, 431238, 1180968, 3225940, 8773036, 23809148, 64388402, 173829458, 467950860, 1257901236, 3373450744, 9035758992
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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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}.
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REFERENCES
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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, E. Fusy and A. Rechnitzer, Counting elements and geodesics in Thompson's group $F$. Arxiv: 0902.0202
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.
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LINKS
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Murray Elder, Table of n, a(n) for n=0..1500
M. Elder, E. Fusy and A. Rechnitzer, Counting elements and geodesics in Thompson's group $F$
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EXAMPLE
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For n=1 there are a(1)=4 elements: x_0, x_0^{-1}, x_1, x_1^{-1}.
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CROSSREFS
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Sequence in context: A095350 A084776 A003212 this_sequence A006817 A003119 A001394
Adjacent sequences: A156942 A156943 A156944 this_sequence A156946 A156947 A156948
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KEYWORD
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nonn
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AUTHOR
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Murray Elder (murrayelder(AT)gmail.com), Feb 19 2009
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