

A334248


Number of distinct acyclic orientations of the edges of an ndimensional cube.


4




OFFSET

0,3


COMMENTS

a(n) is the number of acyclic orientations of the edges of an ndimensional cube, with rotations and reflections of the same orientation not counted.
Except for n=0 and n=2, a(n) can be obtained by substituting 1 for x in the chromatic polynomials given in A334358. This fails for n = 2 because the square when folded diagonally gives a graph with an odd number of vertices. The contribution from this graph needs to be negated when determining the number of acyclic orientations.  Andrew Howroyd, Apr 24 2020


LINKS

Table of n, a(n) for n=0..5.
Matthew Scroggs, Python code to calculate A334248.
Stack Exchange Combinatorial problem: Directed Acyclic Graph
Eric Weisstein's World of Mathematics, Hypercube Graph
Wikipedia, Acyclic orientation


FORMULA

a(n) = Sum_{k=1..2^n} (1)^k * A334358(n, 2^nk)/(n!*2^n) for n >= 3.  Andrew Howroyd, Apr 24 2020


CROSSREFS

Cf. A333418. A334247 is the number of acyclic orientations with rotations and reflections of the same orientation included.
Cf. A334358.
Sequence in context: A214006 A154604 A188798 * A193256 A319038 A227054
Adjacent sequences: A334245 A334246 A334247 * A334249 A334250 A334251


KEYWORD

nonn,more


AUTHOR

Matthew Scroggs, Apr 20 2020


EXTENSIONS

a(5) from Andrew Howroyd, Apr 24 2020


STATUS

approved



