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%I #19 Aug 01 2023 15:00:00
%S 4,24,192,2112,32640,718080,22665216,1031276544,67849629696,
%T 6468240187392,894839431299072,179851071814434816,
%U 52561241074964496384,22351071118387029737472,13837189739906569661841408
%N Number of 4-colorings of the n X n X n triangular grid.
%C The n X n X n triangular grid has n rows with k vertices in row k. 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.
%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>
%F a(n) = 4 * A153467(n).
%Y 4th row of A182797. Cf. A178435, A182788, A182789, A182790, A182791, A182792, A182793, A182794, A182795, A182796.
%K nonn
%O 1,1
%A _Alois P. Heinz_, Dec 02 2010
%E a(15) from _Alois P. Heinz_, Mar 11 2016
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