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

1,2

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

Links

Table of n, a(n) for n=1..16.

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

Example

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

Crossrefs

Sequence in context: A025113 A290956 A089427 * A222691 A254201 A222795

Adjacent sequences: A197561 A197562 A197563 * A197565 A197566 A197567

Keyword

nonn

Author

R. H. Hardin, Oct 16 2011

Status

approved