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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

Table of n, a(n) for n=0..6.

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<<n) \\ Charles R Greathouse IV, Jan 19 2012

CROSSREFS

Cf. A043322, A092258.

Sequence in context: A229100 A060757 A136807 * A132656 A137840 A114561

Adjacent sequences:  A057153 A057154 A057155 * A057157 A057158 A057159

KEYWORD

easy,nice,nonn

AUTHOR

Henry Bottomley, Aug 15 2000

EXTENSIONS

More terms from Vladimir Joseph Stephan Orlovsky, Mar 02 2009

STATUS

approved

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