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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 equal and exactly one upright 2x2x2 triangle having values all different.
4

%I #4 Apr 09 2016 07:29:59

%S 0,0,0,0,0,0,0,0,12,0,0,0,12,1440,0,0,0,12,2961,207360,0,0,0,12,3192,

%T 948561,46448640,0,0,0,12,3195,1460310,526617762,17836277760,0,0,0,12,

%U 3195,1563960,1400351232,562292792592,12328435187712,0,0,0,12,3195

%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 equal and exactly one upright 2x2x2 triangle having values all different.

%C Table starts

%C .0...........0............0.............0.............0.............0

%C .0...........0............0.............0.............0.............0

%C .0..........12...........12............12............12............12

%C .0........1440.........2961..........3192..........3195..........3195

%C .0......207360.......948561.......1460310.......1563960.......1570230

%C .0....46448640....526617762....1400351232....1914775356....2036654646

%C .0.17836277760.562292792592.2894119482336.5984895432180.7699557318624

%H R. H. Hardin, <a href="/A271517/b271517.txt">Table of n, a(n) for n = 1..86</a>

%e Some solutions for n=4 k=4

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

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

%e ...0.1.2....2.1.1....0.1.0....1.1.1....0.0.0....2.1.1....1.1.2....1.2.0

%e ..3.3.2.2..0.3.1.1..2.2.0.0..0.2.2.1..2.1.0.0..2.2.0.0..0.1.0.0..1.3.3.0

%K nonn,tabl

%O 1,9

%A _R. H. Hardin_, Apr 09 2016