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%I #3 Mar 31 2012 12:35:35
%S 1,17,174,2084,35489,950448,42560032
%N Number of nXnXn triangular 1..3 arrays with all 1s connected, all 2s connected, all 3s connected, 1 at the top vertex, 2 at the lower left, and 3 at the lower right
%e All solutions for n=3
%e .....1........1........1........1........1........1........1........1...
%e ....2.1......1.1......2.3......1.3......2.1......1.1......2.3......1.3..
%e ...2.2.3....2.2.3....2.2.3....2.2.3....2.3.3....2.3.3....2.3.3....2.3.3.
%e ------
%e .....1........1........1........1........1........1........1........1...
%e ....2.2......2.2......1.1......1.3......2.1......3.3......3.3......1.2..
%e ...2.2.3....2.3.3....2.1.3....2.1.3....2.1.3....2.2.3....2.3.3....2.2.3.
%e ------
%e .....1...
%e ....3.1..
%e ...2.3.3.
%K nonn
%O 2,2
%A _R. H. Hardin_ Aug 24 2009
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