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A156946
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Geodesic growth sequence for Richard Thompson's group F with the standard generating set x_0, x_1.
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0
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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
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0,2
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COMMENTS
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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}.
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REFERENCES
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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
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LINKS
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EXAMPLE
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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.
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CROSSREFS
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Cf. A156945, the number of elements in F.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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