A267387 Number of acyclic orientations of the Turán graph T(n,7).

1, 1, 2, 6, 24, 120, 720, 5040, 35280, 287280, 2656080, 27422640, 312273360, 3884393520, 52370755920, 704126188080, 10259633739600, 160825241006640, 2696186419390800, 48104638617656880, 909616190783645520, 18163810790066314800, 361758057531039101520

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! / (6 * (1 - log(7/6))^3 * 7^n * (log(7/6))^(n+1)). - Vaclav Kotesovec, Feb 18 2017

Crossrefs

Column k=7 of A267383.

Sequence in context: A179353 A179359 A179366 * A152369 A152387 A152383

Adjacent sequences: A267384 A267385 A267386 * A267388 A267389 A267390

Keyword

nonn

Author

Alois P. Heinz, Jan 13 2016

Status

approved