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A267386 Number of acyclic orientations of the Turán graph T(n,6). 2
1, 1, 2, 6, 24, 120, 720, 4320, 30960, 256320, 2399760, 25022880, 287250480, 3284869680, 41344521840, 566715682800, 8391341277360, 133348995238320, 2262083352430320, 38232720235613520, 689864650481977200, 13221780471876281040, 268029961230742291440 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 31 07:14 EDT 2020. Contains 334747 sequences. (Running on oeis4.)