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

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

%S 1,4,12,94,1604,47877,2261778,187733882,30981880951,9213362077719

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

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

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

%e .........2................0................0................0

%e ........0.0..............3.3..............0.0..............3.2

%e .......0.0.0............0.0.0............0.6.0............0.0.1

%e ......0.3.3.0..........0.3.3.0..........0.0.0.0..........3.1.5.1

%e .....1.1.4.3.0........0.3.4.3.0........0.0.3.3.0........0.0.1.1.0

%e ....1.5.1.3.0.0......0.0.1.1.0.3......0.1.1.4.3.0......0.0.3.4.3.0

%e ...2.2.1.0.0.6.0....0.6.0.5.1.0.3....2.1.5.1.3.0.3....0.6.0.3.3.0.0

%e ..0.0.0.3.0.0.0.0..2.0.0.1.1.2.0.0..0.2.0.1.0.0.3.0..2.0.0.0.0.0.0.0

%K nonn

%O 1,2

%A _R. H. Hardin_ Oct 19 2011