cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A057156 Number of functions from {0,1}^n to {0,1}^n.

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%I A057156 #25 Sep 06 2023 22:38:11
%S A057156 1,4,256,16777216,18446744073709551616,
%T A057156 1461501637330902918203684832716283019655932542976,
%U A057156 39402006196394479212279040100143613805079739270465446667948293404245721771497210611414266254884915640806627990306816
%N A057156 Number of functions from {0,1}^n to {0,1}^n.
%C A057156 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
%D A057156 François Robert, Discrete Iterations: A Metric Study, Springer-Verlag, 1986, p. 167.
%D A057156 Norbert Wiener, Nonlinear Problems in Random Theory, MIT Press Classic, 1958, Lecture 1.
%H A057156 Alois P. Heinz, <a href="/A057156/b057156.txt">Table of n, a(n) for n = 0..8</a>
%F A057156 a(n) = (2^n)^(2^n) = A000312(A000079(n)) = A000079(A036289(n)) = A001146(n)^n = A000722(n) + A057157(n).
%F A057156 Sum_{n>=1} 1/a(n) = A134880. - _Amiram Eldar_, Nov 15 2020
%e A057156 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.
%e A057156 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
%t A057156 lst={};Do[AppendTo[lst,(2^n)^(2^n)],{n,0,8}];lst (* _Vladimir Joseph Stephan Orlovsky_, Mar 02 2009 *)
%o A057156 (PARI) a(n)=1<<(n<<n) \\ _Charles R Greathouse IV_, Jan 19 2012
%Y A057156 Cf. A000079, A000312, A000722, A001146, A036289, A043322, A057157, A092258, A134880.
%K A057156 easy,nice,nonn
%O A057156 0,2
%A A057156 _Henry Bottomley_, Aug 15 2000
%E A057156 More terms from _Vladimir Joseph Stephan Orlovsky_, Mar 02 2009