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%I
%S 1,17,159,1448,16770,293511,8049711
%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, and no value having more than 4 identical values adjacent
%e Some solutions for n=4
%e ......1..........1..........1..........1..........1..........1..........1....
%e .....1.1........2.2........1.1........3.3........1.1........3.3........3.1...
%e ....2.1.3......2.3.2......2.2.1......3.2.3......1.2.2......2.2.3......2.3.1..
%e ...2.1.1.3....2.3.3.3....2.2.1.3....2.2.3.3....2.2.3.3....2.3.3.3....2.3.3.3.
%e ------
%e ......1..........1..........1..........1..........1..........1..........1....
%e .....1.1........3.1........2.1........2.3........2.1........1.1........1.2...
%e ....1.1.3......3.3.1......2.2.2......2.2.3......2.2.3......1.2.1......1.2.3..
%e ...2.2.2.3....2.2.3.3....2.2.3.3....2.3.3.3....2.3.3.3....2.2.2.3....2.2.3.3.
%K nonn
%O 2,2
%A _R. H. Hardin_ Aug 24 2009
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