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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 different.
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%I #3 Apr 01 2016 12:35:45

%S 0,1,72,10716,4023409,3973372776,10282778195346,69615227852939489,

%T 1237061064284160182778,57993308799736991495547414

%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 different.

%C Column 4 of A271194.

%e Some solutions for n=4

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

%e ....1.0......1.0......1.1......1.1......1.2......1.2......1.0......1.2

%e ...1.1.0....2.1.2....2.3.1....0.2.1....1.3.2....3.1.1....2.1.0....1.2.3

%e ..2.1.3.2..1.2.2.0..2.0.3.1..0.3.2.2..4.4.3.2..3.3.1.1..1.2.2.1..0.0.2.2

%Y Cf. A271194.

%K nonn

%O 1,3

%A _R. H. Hardin_, Apr 01 2016