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Number of nXnXn triangular 0..2 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.
0

%I #4 Apr 09 2016 07:28:17

%S 0,0,12,1440,207360,46448640,17836277760,12328435187712,

%T 15780397040271360,38089369770346414080,175515815901756276080640,

%U 1557644360856119698123653120,26796467468679998390760829353984

%N Number of nXnXn triangular 0..2 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 2 of A271517.

%e Some solutions for n=4

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

%e ....1.0......1.2......1.1......1.0......0.0......1.0......1.0......0.1

%e ...0.0.0....2.2.2....1.1.0....2.0.0....0.1.1....1.1.1....1.1.2....1.2.1

%e ..1.2.0.2..0.0.2.1..2.0.1.0..2.0.2.0..1.1.0.2..0.2.2.2..2.2.1.1..2.2.2.2

%Y Cf. A271517.

%K nonn

%O 1,3

%A _R. H. Hardin_, Apr 09 2016