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

%I #10 Jun 14 2014 17:23:55

%S 1,2,5,12,77,720,9259,193296,6058254,309777781,24621646669,

%T 3052707195554

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

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

%e Some solutions with all values 0 to 6 for 8 X 8 X 8:

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

%e ........2.2..............2.2..............2.2..............1.1

%e .......2.4.2............0.1.1............2.5.2............1.6.1

%e ......2.3.4.2..........0.1.6.1..........2.0.2.4..........0.1.1.0

%e .....2.4.2.2.0........2.2.1.1.0........0.2.4.2.2........2.2.2.2.2

%e ....2.0.2.1.1.0......2.4.2.2.2.2......1.1.2.3.4.2......2.4.3.4.4.2

%e ...2.5.2.1.6.1.0....2.4.3.4.4.5.2....1.6.1.2.4.2.0....0.2.4.2.2.5.2

%e ..0.2.2.0.1.1.0.0..0.2.2.2.2.2.2.0..0.1.1.0.2.2.0.0..0.0.2.2.4.2.2.0

%K nonn

%O 1,2

%A _R. H. Hardin_, Oct 17 2011