OFFSET
0,2
COMMENTS
Determinant of character table of elementary Abelian group (C_2)^n.
a(7) has 135 digits. - Jason Earls, Jun 11 2001
Number of functions f:2^X->2^X where X is an n-element set such that f(A) is a subset of A for all A in 2^X (where 2^X denotes the power set of X). - W. Edwin Clark, Nov 06 2003
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..9
Nate Chenette, Reed Phillips, Lara Pudwell, and Manda Riehl, Occurrences of reciprocal sign epistasis in single-and multi-peaked theoretical fitness landscapes, Rose-Hulman and Valparaiso Universities (2022).
F. Echenique, Counting Combinatorial Choice Rules, Games and Economic Behavior, Vol. 58, No. 2 (2007), 231-245.
Lara Pudwell, Nathan Chenette, and Manda Riehl, Statistics on Hypercube Orientations, AMS Special Session on Experimental and Computer Assisted Mathematics, Joint Mathematics Meetings (Denver 2020).
FORMULA
a(n) = 2^Sum_{i=0..n} i*binomial(n, i) = 2^(2^(n-1)*n). - W. Edwin Clark, Nov 06 2003
EXAMPLE
a(2) = 16 because the character table for C_2 X C_2 is / 1 1 1 1 / 1 -1 -1 1 / 1 -1 1 -1 / 1 1-1 -1 / with determinant 16 = (2^2)^(2^1).
a(1) = 2 since 2^{1} = { {}, {1}} and the functions f : 2^{1}->2^{1} satisfying f(A) is a subset of A for all A are g and h where g({})={}, g({1})={} and h({}) = {}, h({1})={1}. - W. Edwin Clark, Nov 06 2003
MATHEMATICA
Table[2^(n 2^(n - 1)), {n, 0, 7}] (* Vincenzo Librandi, Sep 02 2018 *)
PROG
(Magma) [2^(n*2^(n-1)): n in [0..5]]; // Vincenzo Librandi, Sep 02 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Ahmed Fares (ahmedfares(AT)my-deja.com), Jun 05 2001
EXTENSIONS
More terms from Jason Earls, Jun 11 2001
Edited by N. J. A. Sloane, Oct 27 2008 at the suggestion of R. J. Mathar
Offset changed to 0 by Vincenzo Librandi, Sep 02 2018
STATUS
approved