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%I #4 Apr 01 2016 12:37:39
%S 0,0,0,0,1,0,0,1,48,0,0,1,72,3654,0,0,1,72,9168,546604,0,0,1,72,10716,
%T 2507552,173123868,0,0,1,72,10794,4023409,1585190304,120268341210,0,0,
%U 1,72,10794,4396148,3973372776,2396160624384,186894023900240,0,0,1,72
%N T(n,k)=Number of nXnXn triangular 0..k arrays with new values introduced in sequential zero-upwards order and exactly one upright 2x2x2 triangle having values all different.
%C Table starts
%C .0............0.............0..............0..............0..............0
%C .0............1.............1..............1..............1..............1
%C .0...........48............72.............72.............72.............72
%C .0.........3654..........9168..........10716..........10794..........10794
%C .0.......546604.......2507552........4023409........4396148........4426829
%C .0....173123868....1585190304.....3973372776.....5372968836.....5718522642
%C .0.120268341210.2396160624384.10282778195346.19590379147806.24423371106474
%H R. H. Hardin, <a href="/A271194/b271194.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......0.1......1.0......0.1......1.1......1.1......1.1......1.0
%e ...3.1.1....0.0.2....2.3.3....0.1.0....1.0.2....1.2.2....2.1.3....0.0.2
%e ..0.0.1.4..2.0.2.2..2.2.3.3..2.2.2.1..1.1.0.2..2.1.1.3..2.0.0.1..0.3.1.1
%K nonn,tabl
%O 1,9
%A _R. H. Hardin_, Apr 01 2016
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