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 A057156 Number of functions from {0,1}^n to {0,1}^n. 5
 1, 4, 256, 16777216, 18446744073709551616, 1461501637330902918203684832716283019655932542976, 39402006196394479212279040100143613805079739270465446667948293404245721771497210611414266254884915640806627990306816 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS 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 REFERENCES F. Robert, Discrete Iterations, Springer-Verlag, 1986, p. 167. Norbert Wiener, Nonlinear Problems in Random Theory,MIT Press Classic, 1958, Lecture 1. LINKS FORMULA a(n) = (2^n)^(2^n) = A000312(A000079(n)) = A000079(A036289(n)) = A001146(n)^n = A000722(n) + A057157(n). EXAMPLE 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. MATHEMATICA lst={}; Do[AppendTo[lst, (2^n)^(2^n)], {n, 0, 8}]; lst (* Vladimir Joseph Stephan Orlovsky, Mar 02 2009 *) PROG (PARI) a(n)=1<<(n<

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Last modified January 26 23:05 EST 2020. Contains 331289 sequences. (Running on oeis4.)