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

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

%S 1,5,14,63,513,10097,259230,11938480,1034835441,141000000947

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

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

%e ........2.1..............0.0..............0.2..............2.2

%e .......2.2.3............0.0.0............0.2.2............0.0.0

%e ......0.4.1.1..........0.0.6.0..........0.0.4.0..........0.0.6.0

%e .....0.2.2.0.1........0.5.0.0.0........0.0.2.2.1........0.5.0.0.0

%e ....0.0.2.0.2.2......1.2.0.2.2.0......0.6.0.2.1.3......1.2.0.2.2.1

%e ...0.6.0.5.0.2.1....1.2.2.1.2.4.2....2.0.0.5.0.2.1....1.2.2.1.2.4.2

%e ..0.0.0.0.0.0.0.1..1.0.1.3.1.0.2.2..2.2.0.0.0.2.2.0..1.0.1.3.1.0.2.2

%K nonn

%O 1,2

%A _R. H. Hardin_ Oct 18 2011