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A267384
Number of acyclic orientations of the Turán graph T(n,4).
2
1, 1, 2, 6, 24, 96, 504, 3216, 24024, 177816, 1538424, 15108216, 165392664, 1793999256, 21693217464, 288019921656, 4154515368024, 59434596913656, 924041894967864, 15469081577068056, 276917744041735704, 4921195271561687256, 93549435117715431864
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
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! / (3 * (1-log(4/3))^(3/2) * 4^n * (log(4/3))^(n+1)). - Vaclav Kotesovec, Feb 18 2017
CROSSREFS
Column k=4 of A267383.
Sequence in context: A147895 A070945 A152320 * A152327 A152314 A152331
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jan 13 2016
STATUS
approved