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

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

%S 1,4,9,20,74,379,3003,38251,799417,26052840,1338355732,107392201905

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

%C Every 0 is next to 0 1's, every 1 is next to 1 4'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 8X8X8

%e .........2................0................1................2

%e ........0.0..............0.0..............1.4..............0.0

%e .......0.0.2............2.0.0............1.1.1............0.0.0

%e ......0.0.2.1..........1.2.0.0..........4.1.3.2..........0.0.6.0

%e .....0.5.2.1.4........4.1.2.5.0........1.1.2.0.0........0.5.0.0.2

%e ....0.0.0.2.1.1......1.1.2.0.0.0......2.2.2.0.0.0......0.0.2.2.3.1

%e ...0.0.6.0.3.1.1....1.1.3.0.0.6.0....0.0.0.5.0.6.0....0.0.2.1.1.1.4

%e ..2.0.0.0.2.1.4.1..1.4.1.2.0.0.0.0..0.0.0.0.0.0.0.2..0.0.2.1.4.1.1.1

%K nonn

%O 1,2

%A _R. H. Hardin_ Oct 18 2011