A334247 Number of acyclic orientations of the edges of an n-dimensional cube.

1, 2, 14, 1862, 193270310, 47171704165698393638

Offset

0,2

Comments

a(n) is the absolute value of the chromatic polynomial of the n-hypercube graph evaluated at -1.

Links

Table of n, a(n) for n=0..5.

David Eppstein, 14 acyclic orientations of a square

Eric Weisstein's World of Mathematics, Hypercube Graph

Formula

a(n) = Sum_{k=1..2^n} (-1)^(2^n-k) * k! * A334159(n, k). - Andrew Howroyd, Apr 21 2020

a(n) = |Sum_{k=0..2^n} (-1)^k * A334278(n, k)|. - Peter Kagey, Oct 13 2020

Example

For n=2, there are 14 ways to orient the edges of a square without cycles (see links).

Crossrefs

Cf. A334248 is the number of acyclic orientations with rotations and reflections of the same orientation excluded.

Cf. A140986, A158348, A296914, A334159, A334278.

Cf. A033815 (cross-polytope), A058809 (wheel), A338152 (demihypercube), A338153 (prism), A338154 (antiprism).

Sequence in context: A347908 A227403 A156736 * A277288 A296412 A296410

Adjacent sequences: A334244 A334245 A334246 * A334248 A334249 A334250

Keyword

nonn,more

Author

Matthew Scroggs, Apr 20 2020

Extensions

a(5) from Andrew Howroyd, Apr 23 2020

Status

approved