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Number of n X n X n triangular 0..2 arrays with new values introduced in sequential zero-upwards order and exactly one 2 X 2 X 2 triangle having values all different.
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%I #6 Sep 03 2022 22:17:01

%S 0,1,44,2529,239700,41288768,13536514992,8663986363705,

%T 10993523599196564,27931583281337318808,143073130086443218161862,

%U 1484701531903686677651991942,31325520846551262114728413158870

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

%C Column 2 of A271141.

%e Some solutions for n=4

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

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

%e ...1.0.2....1.2.2....1.1.2....1.2.2....2.2.2....1.2.0....2.2.0....1.1.1

%e ..1.0.1.2..1.2.2.2..1.2.2.2..1.1.1.1..2.0.2.1..2.1.2.0..2.2.0.2..0.1.0.2

%Y Cf. A271141.

%K nonn

%O 1,3

%A _R. H. Hardin_, Mar 31 2016