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

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

%S 1,4,21,268,5693,304842,29792961,5250711122,2139491424754

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

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

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

%e .......1.3............1.3............1.3............1.1............0.0

%e ......1.4.1..........1.4.1..........1.4.1..........0.3.1..........0.6.0

%e .....0.3.1.2........1.3.1.0........3.1.2.2........0.5.0.1........0.0.0.0

%e ....0.1.0.0.0......0.0.0.0.0......1.2.0.0.0......0.0.0.3.1......0.0.1.0.2

%e ...0.5.0.0.6.0....3.1.5.0.6.0....0.0.5.0.6.0....0.6.0.1.4.1....0.5.3.1.1.3

%e ..2.0.0.0.0.0.2..1.1.0.0.0.0.2..2.0.0.0.0.0.2..2.0.0.2.1.3.1..0.0.0.1.4.1.1

%K nonn

%O 1,2

%A _R. H. Hardin_ Oct 20 2011