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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 4,0,0,0,1,0,0 for x = 0,1,2,3,4,5,6.
0

%I #6 Sep 25 2021 10:58:21

%S 1,7,39,437,8925,305779,18569865,1972604754,365315073334,

%T 118431758924590

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

%C Every 0 is next to 0 4's, every 1 is next to 1 0's, every 2 is next to 2 0's, every 3 is next to 3 0'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 7 X 7 X 7

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

%e .......2.1............0.3............0.0............0.0............3.2

%e ......0.1.4..........0.0.0..........0.0.0..........0.0.0..........0.0.3

%e .....2.3.1.1........0.0.6.0........0.6.0.0........0.0.5.0........0.6.0.0

%e ....3.0.0.3.0......2.3.0.0.0......3.0.0.3.1......1.2.3.0.0......0.0.0.3.1

%e ...0.0.6.0.5.0....0.1.1.3.5.0....2.0.5.2.4.1....1.4.2.0.6.0....3.5.0.3.4.1

%e ..1.3.0.0.0.0.2..1.1.4.1.0.0.2..0.3.0.0.1.1.0..0.1.1.0.0.0.0..0.0.0.0.1.1.0

%K nonn

%O 1,2

%A _R. H. Hardin_ Dec 30 2011