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A057156
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Number of functions from {0,1}^n to {0,1}^n.
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9
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1, 4, 256, 16777216, 18446744073709551616, 1461501637330902918203684832716283019655932542976, 39402006196394479212279040100143613805079739270465446667948293404245721771497210611414266254884915640806627990306816
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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 subdivisions of the Brownian motion on the unit interval at the n-th stage of subdivision. - Stephen Crowley, Apr 12 2007
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REFERENCES
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François Robert, Discrete Iterations: A Metric Study, Springer-Verlag, 1986, p. 167.
Norbert Wiener, Nonlinear Problems in Random Theory, MIT Press Classic, 1958, Lecture 1.
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LINKS
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FORMULA
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EXAMPLE
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a(1)=4 since the possibilities are f(0)=0, f(1)=0; f(0)=0, f(1)=1; f(0)=1, f(1)=0; f(0)=1, f(1)=1.
For n=3: we need to count maps from a set with 8 points to a set with 8 points. There are 8^8 such functions, that is, a(3) = 8^8 = 2^24 = 16777216. - N. J. A. Sloane, Mar 05 2023
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MATHEMATICA
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PROG
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CROSSREFS
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KEYWORD
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easy,nice,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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