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Number of n X n X n 0..6 triangular arrays with each element x equal to the number its neighbors equal to 5,1,2,1,2,2,0 for x=0,1,2,3,4,5,6.
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%I #7 Jan 20 2024 15:09:29

%S 1,5,20,278,4448,175624,12844710,1595718051,427062500640

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

%C Every 0 is next to 0 5'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 2's, every 6 is next to 6 0's.

%e Some solutions with all values from 0 to 6 for 7 X 7 X 7

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

%e .......2.2............0.0............0.0............2.2............0.0

%e ......2.0.2..........0.6.0..........0.6.0..........2.5.2..........0.6.0

%e .....0.2.4.2........0.0.0.1........1.0.0.0........2.4.2.0........1.0.0.0

%e ....0.0.2.5.2......2.2.2.2.1......1.2.2.2.2......2.0.2.0.0......1.2.2.2.2

%e ...0.6.0.2.2.1....2.5.4.5.2.3....3.2.0.4.5.2....1.2.2.0.6.0....3.2.5.4.0.2

%e ..0.0.0.1.1.3.1..0.2.2.2.2.1.1..1.1.2.2.2.2.0..1.3.1.1.0.0.0..1.1.2.2.2.2.0

%K nonn

%O 1,2

%A _R. H. Hardin_, Oct 20 2011