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%I #6 Mar 08 2023 11:58:29
%S 1,5,20,208,3516,108850,6900201,776174640,167355580505,68493666999406
%N Number of n X n X n 0..6 triangular arrays with each element x equal to the number its neighbors equal to 3,1,2,1,2,0,2 for x=0,1,2,3,4,5,6.
%C Every 0 is next to 0 3's, every 1 is next to 1 1'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 2's.
%e Some solutions with all values from 0 to 6 for 7 X 7 X 7
%e ........0..............0..............1..............0..............0
%e .......0.2............0.0............2.1............1.0............0.0
%e ......0.2.2..........0.5.0..........2.2.3..........1.2.2..........0.5.0
%e .....0.0.4.1........1.0.2.2........0.4.1.1........0.2.6.2........1.0.2.2
%e ....0.0.2.2.1......3.1.2.6.2......0.2.2.0.0......2.4.2.2.0......3.1.2.6.2
%e ...0.5.2.6.2.3....1.2.4.2.2.1....0.2.6.2.5.0....2.2.1.0.5.0....1.2.4.2.2.0
%e ..0.0.0.2.2.1.1..1.2.2.0.0.0.1..1.1.2.2.0.0.0..1.1.3.1.0.0.0..1.2.2.1.1.0.0
%K nonn
%O 1,2
%A _R. H. Hardin_, Dec 29 2011