

A178435


Number of acyclic orientations of the Triangle Graph of order n.


11



1, 6, 162, 19602, 10619910, 25753129470, 279488630719746, 13573527285845525634, 2949851294016821586137934, 2868652614504623418332698354038, 12483073717920041560887416137620435882, 243068197882943244196175524589364487906969746, 21178547618859581967063811182618272071362317831449326
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OFFSET

1,2


COMMENTS

The Triangle Graph of order n has n rows with i vertices in row i. Each vertex is connected to the neighbors in the same row and up to two vertices in each of the neighboring rows. The Graph has A000217(n) vertices and 3*A000217(n1) edges altogether.
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

Table of n, a(n) for n=1..13.
Richard P. Stanley, Acyclic Orientations of Graphs, Discrete Mathematics, 5 (1973), pages 171178, doi:10.1016/0012365X(73)901088
Eric Weisstein's World of Mathematics, Triangle Graph
Wikipedia, Chromatic polynomial


CROSSREFS

Cf. A182797, A182788, A182789, A182790, A182791, A182792, A182793, A182794, A182795, A182796, A182798, A000217.
Sequence in context: A280477 A078535 A177781 * A183254 A143534 A104729
Adjacent sequences: A178432 A178433 A178434 * A178436 A178437 A178438


KEYWORD

hard,nonn


AUTHOR

Alois P. Heinz, Dec 21 2010


STATUS

approved



