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Number of nXnXn triangular 0..4 arrays with new values introduced in sequential zero-upwards order and exactly one upright 2x2x2 triangle having values all equal and exactly one upright 2x2x2 triangle having values all different.
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%I #3 Apr 09 2016 07:29:01

%S 0,0,12,3192,1460310,1400351232,2894119482336,13177722597521472,

%T 135132206434712566080

%N Number of nXnXn triangular 0..4 arrays with new values introduced in sequential zero-upwards order and exactly one upright 2x2x2 triangle having values all equal and exactly one upright 2x2x2 triangle having values all different.

%C Column 4 of A271517.

%e Some solutions for n=4

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

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

%e ...0.0.0....0.0.1....1.0.1....1.1.1....0.0.1....1.1.0....1.2.3....2.0.1

%e ..2.0.0.2..0.2.1.2..0.0.0.2..2.3.1.3..2.1.1.1..2.2.0.2..1.2.3.3..2.0.0.1

%Y Cf. A271517.

%K nonn

%O 1,3

%A _R. H. Hardin_, Apr 09 2016