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%I #4 Apr 02 2016 20:29:18
%S 0,0,0,0,0,0,0,0,27,0,0,0,64,3969,0,0,0,76,19200,900963,0,0,0,77,
%T 33672,9523200,401227533,0,0,0,77,38571,28240419,10151116800,
%U 378139318893,0,0,0,77,39210,43105569,56147799704,24976569139200,781827640754454,0,0,0,77
%N T(n,k)=Number of nXnXn triangular 0..k arrays with new values introduced in sequential zero-upwards order and exactly one inverted 2x2x2 triangle having values all different.
%C Table starts
%C .0.........0...........0...........0............0............0............0
%C .0.........0...........0...........0............0............0............0
%C .0........27..........64..........76...........77...........77...........77
%C .0......3969.......19200.......33672........38571........39210........39237
%C .0....900963.....9523200....28240419.....43105569.....48347502.....49235880
%C .0.401227533.10151116800.56147799704.131856310191.187829420863.209021374705
%H R. H. Hardin, <a href="/A271246/b271246.txt">Table of n, a(n) for n = 1..99</a>
%e Some solutions for n=4 k=4
%e .....0........0........0........0........0........0........0........0
%e ....1.2......1.2......1.0......1.1......1.1......1.2......1.0......1.2
%e ...2.1.0....1.1.3....1.0.1....0.2.0....2.2.3....1.2.0....2.0.3....1.1.3
%e ..1.1.2.1..0.1.0.0..2.1.3.3..3.3.0.0..1.3.0.2..1.1.3.4..0.2.1.0..3.3.4.1
%K nonn,tabl
%O 1,9
%A _R. H. Hardin_, Apr 02 2016
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