%I #6 Apr 26 2023 10:06:09
%S 1,4,4,9,253,1866,41286,1769077,63965087,8815768229
%N Number of n X n X n 0..6 triangular arrays with each element x equal to the number its neighbors equal to 2,0,1,1,1,1,1 for x=0,1,2,3,4,5,6.
%C Every 0 is next to 0 2's, every 1 is next to 1 0's, every 2 is next to 2 1's, every 3 is next to 3 1's, every 4 is next to 4 1's, every 5 is next to 5 1's, every 6 is next to 6 1's.
%e Some solutions with all values from 0 to 6 for 7 X 7 X 7
%e ........0..............0..............1..............0..............1
%e .......1.1............1.1............1.0............1.1............0.1
%e ......1.4.2..........1.6.1..........1.4.0..........2.4.1..........0.4.1
%e .....0.1.3.1........0.1.1.0........0.1.1.1........1.3.1.0........1.1.1.0
%e ....1.1.5.1.0......1.1.5.1.1......1.1.5.3.2......0.1.5.1.1......2.3.5.1.1
%e ...1.6.1.1.4.0....1.4.1.3.4.1....1.6.1.1.4.1....0.4.1.1.6.1....1.4.1.1.6.1
%e ..0.1.1.0.1.1.1..1.0.0.1.2.1.0..0.1.1.0.1.1.0..1.1.1.0.1.1.0..0.1.1.0.1.1.0
%K nonn
%O 1,2
%A _R. H. Hardin_, Oct 20 2011