%I #4 Mar 31 2016 09:24:40
%S 0,0,0,0,1,0,0,1,44,0,0,1,56,2529,0,0,1,56,4560,239700,0,0,1,56,4890,
%T 625280,41288768,0,0,1,56,4899,778256,158875520,13536514992,0,0,1,56,
%U 4899,797680,245558565,78509767680,8663986363705,0,0,1,56,4899,798370
%N T(n,k)=Number of nXnXn triangular 0..k arrays with new values introduced in sequential zero-upwards order and exactly one 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............44.............56..............56..............56..............56
%C .0..........2529...........4560............4890............4899............4899
%C .0........239700.........625280..........778256..........797680..........798370
%C .0......41288768......158875520.......245558565.......269282132.......271950103
%C .0...13536514992....78509767680....158940847866....197805084468....206442174684
%C .0.8663986363705.77552409009664.214449879142050.321887622195271.362418477051236
%H R. H. Hardin, <a href="/A271141/b271141.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 ....0.1......1.1......1.0......1.1......0.0......0.0......1.1......1.2
%e ...1.1.0....1.2.2....2.1.1....0.0.1....1.1.2....1.2.0....1.1.2....2.2.3
%e ..0.1.2.0..1.1.1.0..3.1.0.0..0.2.1.0..2.2.2.1..2.2.0.1..1.0.2.3..2.3.3.3
%K nonn,tabl
%O 1,9
%A _R. H. Hardin_, Mar 31 2016