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

%I #8 Oct 20 2014 17:08:49

%S 1,4,42,801,32906,2686539,448034446,157510353675,113936781145405

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

%C Every 0 is next to zero 4's, every 1 is next to one 2, every 2 is next to two 0's, every 3 is next to three 0's, every 4 is next to four 2's, every 5 is next to five 0's, every 6 is next to six 0's.

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

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

%e .......2.0............0.0............0.0............2.0............0.0

%e ......4.2.3..........0.6.0..........0.1.2..........4.2.0..........0.0.0

%e .....2.2.0.0........3.0.0.0........2.0.0.1........2.2.3.0........0.6.0.2

%e ....0.0.1.5.0......1.0.5.0.0......4.2.5.0.0......0.0.0.5.0......3.0.0.2.4

%e ...0.6.0.0.0.2....0.2.2.0.5.3....2.2.0.0.6.0....0.0.6.0.0.2....2.0.5.3.2.2

%e ..2.0.0.0.0.1.1..0.2.4.2.0.0.0..0.0.3.0.0.0.0..0.0.0.0.3.1.1..0.1.0.0.0.0.0

%K nonn,more

%O 1,2

%A _R. H. Hardin_, Oct 19 2011