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Number of nXnXn 0..6 triangular arrays with each element x equal to the number its neighbors equal to 4,3,2,0,1,0,2 for x=0,1,2,3,4,5,6
0

%I #13 Mar 31 2012 12:36:24

%S 1,2,20,252,7403,421616,52543529,13657426873,7262057176754

%N Number of nXnXn 0..6 triangular arrays with each element x equal to the number its neighbors equal to 4,3,2,0,1,0,2 for x=0,1,2,3,4,5,6

%C Every 0 is next to 0 4's, every 1 is next to 1 3's, every 2 is next to 2 2's, every 3 is next to 3 0's, every 4 is next to 4 1's, every 5 is next to 5 0's, every 6 is next to 6 2's

%e Some solutions with all values 0 to 6 for 8X8X8

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

%e ........2.2..............2.2..............0.0..............2.2

%e .......2.6.2............2.6.2............3.3.1............2.6.2

%e ......0.2.2.0..........0.2.2.0..........0.0.1.4..........0.2.2.0

%e .....0.5.0.5.0........0.5.0.1.3........0.1.0.1.1........0.5.0.0.3

%e ....1.0.0.0.0.1......0.0.0.0.0.0......2.2.3.0.3.0......0.0.0.1.3.0

%e ...0.3.1.1.3.3.0....0.3.1.1.3.5.0....2.6.2.0.5.0.2....0.5.3.1.1.0.0

%e ..0.0.1.4.1.0.3.0..0.1.1.4.1.0.0.0..0.2.2.0.0.0.2.2..0.0.0.1.4.1.3.0

%K nonn

%O 1,2

%A _R. H. Hardin_ Oct 17 2011