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%I #17 Aug 01 2023 14:30:24
%S 1,6,162,19602,10619910,25753129470,279488630719746,
%T 13573527285845525634,2949851294016821586137934,
%U 2868652614504623418332698354038,12483073717920041560887416137620435882,243068197882943244196175524589364487906969746,21178547618859581967063811182618272071362317831449326
%N Number of acyclic orientations of the n X n X n triangular grid.
%C The n X n X n triangular grid 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(n-1) edges altogether.
%C 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.
%H Richard P. Stanley, Acyclic Orientations of Graphs, Discrete Mathematics, 5 (1973), pages 171-178, doi:<a href="http://dx.doi.org/10.1016/0012-365X(73)90108-8">10.1016/0012-365X(73)90108-8</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Chromatic_polynomial">Chromatic polynomial</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Lattice_graph#Other_kinds">Triangular grid graph</a>
%Y Cf. A182797, A182788, A182789, A182790, A182791, A182792, A182793, A182794, A182795, A182796, A182798, A000217.
%K hard,nonn
%O 1,2
%A _Alois P. Heinz_, Dec 21 2010
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