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

%I #5 Mar 31 2012 12:36:31

%S 1,5,20,284,4771,199564,15833279,2206064568,659395510659

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

%C Every 0 is next to 0 4's, every 1 is next to 1 1's, every 2 is next to 2 2's, every 3 is next to 3 1'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 from 0 to 6 for 7X7X7

%e ........1..............0..............0..............0..............1

%e .......1.0............2.2............2.2............0.0............0.1

%e ......0.5.0..........2.6.2..........2.6.2..........0.5.1..........1.3.0

%e .....0.0.0.0........1.2.2.1........0.2.2.1........0.0.0.1........1.4.1.0

%e ....0.1.1.2.2......1.4.1.0.1......0.0.1.4.1......0.1.1.2.2......2.2.1.0.0

%e ...1.3.4.2.6.2....0.3.1.0.5.0....0.5.0.1.3.0....1.3.4.2.6.2....2.6.2.0.5.0

%e ..1.3.1.1.2.2.0..1.1.0.0.0.0.0..1.1.0.0.0.1.1..1.0.1.1.2.2.0..0.2.2.0.0.1.1

%K nonn

%O 1,2

%A _R. H. Hardin_ Oct 20 2011