%I #8 Oct 28 2014 03:40:38
%S 1,4,22,216,4565,170743,11661907,1488001671,356058730204
%N Number of n X n X n 0..6 triangular arrays with each element x equal to the number of its neighbors equal to 6,0,1,0,0,0,1 for x=0,1,2,3,4,5,6.
%C Every 0 is next to zero 6's, every 1 is next to one 0, every 2 is next to two 1's, every 3 is next to three 0's, every 4 is next to four 0's, every 5 is next to five 0's, every 6 is next to six 1's.
%e Some solutions with all values from 0 to 6 for 7 X 7 X 7:
%e ........0..............0..............0..............0..............0
%e .......0.0............0.0............0.0............0.4............0.0
%e ......0.5.0..........3.0.0..........0.4.0..........0.0.0..........0.4.0
%e .....0.2.0.0........0.2.4.0........0.3.1.1........0.0.4.0........0.3.2.0
%e ....1.1.1.4.0......1.1.1.0.0......0.0.1.6.1......0.0.2.1.1......0.0.1.1.1
%e ...1.6.1.2.0.3....1.6.1.3.5.0....0.5.2.1.1.0....0.5.3.1.6.1....0.5.3.1.6.1
%e ..0.1.1.0.0.3.0..0.1.1.0.0.0.0..0.0.0.0.1.1.1..0.0.0.0.1.1.0..0.0.0.0.1.1.0
%K nonn,more
%O 1,2
%A _R. H. Hardin_, Oct 19 2011
