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Search: id:A057156
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| A057156 |
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Number of functions from {0,1}^n to {0,1}^n. |
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+0
6
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| 1, 4, 256, 16777216, 18446744073709551616, 1461501637330902918203684832716283019655932542976, 39402006196394479212279040100143613805079739270465446667948293404245721771497210\ 611414266254884915640806627990306816
(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 subdivisions of the Brownian motion on the unit interval at the n-th stage of subdivision. - Stephen Crowley (crow(AT)crowlogic.net), Apr 12 2007
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REFERENCES
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F. Robert, Discrete Iterations, Springer-Verlag, 1986, p. 167.
Norbert Wiener, Nonlinear Problems in Random Theory,MIT Press Classic, 1958, Lecture 1.
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FORMULA
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a(n) =(2^n)^(2^n) =A000312(A000079(n)) =A000079(A036289(n)) =A001146(n)^n =A000722(n)+A057157(n)
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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.
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MATHEMATICA
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lst={}; Do[AppendTo[lst, (2^n)^(2^n)], {n, 0, 8}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Mar 02 2009]
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CROSSREFS
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Cf. A043322, A092258.
Sequence in context: A122249 A060757 A136807 this_sequence A132656 A137840 A114561
Adjacent sequences: A057153 A057154 A057155 this_sequence A057157 A057158 A057159
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KEYWORD
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easy,nice,nonn
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), Aug 15 2000
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EXTENSIONS
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Added more terms, Mathematica. - Vladimir Orlovsky (4vladimir(AT)gmail.com), Mar 02 2009
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