A267386 Number of acyclic orientations of the Turán graph T(n,6).

1, 1, 2, 6, 24, 120, 720, 4320, 30960, 256320, 2399760, 25022880, 287250480, 3284869680, 41344521840, 566715682800, 8391341277360, 133348995238320, 2262083352430320, 38232720235613520, 689864650481977200, 13221780471876281040, 268029961230742291440

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! / (5 * (1 - log(6/5))^(5/2) * 6^n * (log(6/5))^(n+1)). - Vaclav Kotesovec, Feb 18 2017

Crossrefs

Column k=6 of A267383.

Sequence in context: A179358 A179365 A070947 * A215718 A060727 A152350

Adjacent sequences: A267383 A267384 A267385 * A267387 A267388 A267389

Keyword

nonn

Author

Alois P. Heinz, Jan 13 2016

Status

approved