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

%I #4 Mar 31 2012 12:36:31

%S 1,1,4,23,108,3747,135196,4459381,755829713,172047582057

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

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

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

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

%e ........1.0..............0.0..............0.0..............1.1

%e .......1.4.1............0.6.0............0.6.0............1.4.1

%e ......3.1.0.0..........0.0.0.0..........0.0.0.0..........2.3.0.0

%e .....2.1.0.6.0........0.5.1.1.0........0.5.0.0.0........3.1.1.5.0

%e ....3.1.4.0.0.0......1.0.0.4.0.1......0.0.1.4.1.1......1.1.4.0.0.0

%e ...1.1.1.1.5.0.0....1.4.1.1.1.1.4....1.4.1.1.1.1.4....4.1.0.1.0.6.0

%e ..1.4.1.0.0.0.0.0..0.0.1.3.2.3.1.1..0.1.1.3.2.3.1.1..1.1.0.0.0.0.0.0

%K nonn

%O 1,3

%A _R. H. Hardin_ Oct 18 2011