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Number of nXnXn triangular 0..3 arrays with new values introduced in sequential zero-upwards order and exactly one 2x2x2 triangle having values all different.
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%I #3 Mar 31 2016 09:22:47

%S 0,1,56,4560,625280,158875520,78509767680,77552409009664,

%T 155738737883810688,642865213102166747136,5496169383763345236125056

%N Number of nXnXn triangular 0..3 arrays with new values introduced in sequential zero-upwards order and exactly one 2x2x2 triangle having values all different.

%C Column 3 of A271141.

%e Some solutions for n=4

%e .....0........0........0........0........0........0........0........0

%e ....0.0......0.1......1.2......1.0......1.2......0.0......1.2......1.2

%e ...0.1.0....2.1.0....1.2.2....0.1.1....2.2.1....1.1.2....1.2.3....0.1.2

%e ..2.2.1.0..1.2.1.1..2.2.3.2..2.1.1.0..2.2.1.3..2.2.2.1..2.2.2.2..2.0.1.1

%Y Cf. A271141.

%K nonn

%O 1,3

%A _R. H. Hardin_, Mar 31 2016