A197564 Number of n X n X n 0..6 triangular arrays with each element equal to the number its zero neighbors.

1, 3, 4, 18, 51, 266, 1518, 11396, 111218, 1345019, 21178437, 420441727, 10691248879, 346431341394, 14306876354446, 754052504644414

Offset: 1

Author

R. H. Hardin, Oct 16 2011

Keywords

• nonn

Comments

Also the number of maximal independent vertex sets (and minimal vertex covers) in the (n-1)-triangular grid graph. - Eric W. Weisstein, Jun 14 and Aug 07 2017

Examples

			Some solutions for 5 X 5 X 5:
......1..........0..........0..........0..........0..........1..........0
.....1.0........2.2........1.2........2.1........1.2........0.2........2.2
....1.2.2......0.2.0......1.1.0......0.1.1......1.1.0......1.2.0......1.0.1
...0.2.0.2....2.2.2.2....0.2.2.2....2.2.1.0....0.1.2.2....1.1.1.2....1.2.2.1
..1.1.1.2.0..0.2.0.2.0..1.2.0.2.0..1.0.1.1.1..1.1.1.0.1..1.0.1.1.0..0.2.0.2.0
		

Links

• Eric Weisstein's World of Mathematics, Minimal Vertex Cover
• Eric Weisstein's World of Mathematics, Maximal Independent Vertex Set
• Eric Weisstein's World of Mathematics, Triangular Grid Graph