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

%I #6 Mar 31 2012 12:36:30

%S 1,5,14,63,536,15648,545796,50029471,6569786146

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

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

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

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

%e ........1.1..............1.1..............2.2..............2.2

%e .......1.6.1............1.6.1............2.0.2............2.5.2

%e ......0.1.1.0..........0.1.1.0..........3.2.3.2..........0.2.3.2

%e .....1.2.2.2.0........0.2.2.2.1........0.2.3.4.2........0.2.3.4.2

%e ....2.2.3.3.2.2......2.2.3.3.2.2......1.1.2.3.3.2......1.1.2.3.3.2

%e ...2.0.3.4.3.5.2....2.5.3.4.3.0.2....1.6.1.2.2.5.2....1.6.1.2.2.0.2

%e ..0.2.2.2.2.2.2.0..0.2.2.2.2.2.2.0..0.1.1.0.0.2.2.0..0.1.1.0.1.2.2.0

%K nonn

%O 1,2

%A _R. H. Hardin_ Oct 17 2011