A267389 Number of acyclic orientations of the Turán graph T(n,9).

1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3265920, 33022080, 369774720, 4536362880, 60451816320, 869007242880, 13397819541120, 220448163358080, 3854801333416320, 67295207974942080, 1248445283166184320, 24512281966435294080, 507579925622189454720

Offset

0,3

Comments

An acyclic orientation is an assignment of a direction to each edge such that no cycle in the graph is consistently oriented. Stanley showed that the number of acyclic orientations of a graph G is equal to the absolute value of the chromatic polynomial X_G(q) evaluated at q=-1.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..450

Richard P. Stanley, Acyclic Orientations of Graphs, Discrete Mathematics, 5 (1973), pages 171-178, doi:10.1016/0012-365X(73)90108-8

Wikipedia, Turán graph

Formula

a(n) ~ n! / (8 * (1 - log(9/8))^4 * 9^n * (log(9/8))^(n+1)). - Vaclav Kotesovec, Feb 18 2017

Crossrefs

Column k=9 of A267383.

Sequence in context: A154657 A179361 A179368 * A152693 A152712 A152707

Adjacent sequences: A267386 A267387 A267388 * A267390 A267391 A267392

Keyword

nonn

Author

Alois P. Heinz, Jan 13 2016

Status

approved