A197054 T(n,k)=Number of nXk 0..4 arrays with each element equal to the number of its horizontal and vertical zero neighbors.

1, 2, 2, 2, 2, 2, 3, 4, 4, 3, 4, 6, 10, 6, 4, 5, 10, 18, 18, 10, 5, 7, 16, 38, 42, 38, 16, 7, 9, 26, 78, 108, 108, 78, 26, 9, 12, 42, 156, 274, 358, 274, 156, 42, 12, 16, 68, 320, 692, 1132, 1132, 692, 320, 68, 16, 21, 110, 654, 1754, 3580, 4468, 3580, 1754, 654, 110, 21, 28

Offset: 1

Author

R. H. Hardin, Oct 09 2011

Keywords

• nonn
• tabl

Comments

Every 0 is next to 0 0'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 0's

Also, the number of maximal independent vertex sets in the grid graph P_n X P_k. - Andrew Howroyd, May 16 2017

Examples

			Table starts
..1...2....2.....3......4.......5........7.........9.........12..........16
..2...2....4.....6.....10......16.......26........42.........68.........110
..2...4...10....18.....38......78......156.......320........654........1326
..3...6...18....42....108.....274......692......1754.......4442.......11248
..4..10...38...108....358....1132.....3580.....11382......36270......114992
..5..16...78...274...1132....4468....17742.....70616.....281202.....1117442
..7..26..156...692...3580...17742....88056....439338....2192602....10912392
..9..42..320..1754..11382...70616...439338...2745186...17155374...106972582
.12..68..654..4442..36270..281202..2192602..17155374..134355866..1049189170
.16.110.1326.11248.114992.1117442.10912392.106972582.1049189170.10264692132
...
Some solutions for n=6 k=4
..0..2..1..0....0..2..0..1....2..0..2..0....0..3..0..2....0..2..1..0
..2..0..1..2....1..1..1..1....0..2..1..1....2..0..4..0....3..0..1..2
..1..1..2..0....1..0..2..0....2..1..0..2....1..2..0..2....0..3..1..0
..0..3..0..3....1..1..1..1....0..2..2..0....0..1..1..1....2..0..1..2
..3..0..4..0....0..3..0..2....3..0..1..2....1..1..1..0....1..1..2..0
..0..3..0..2....2..0..3..0....0..2..1..0....1..0..1..1....0..2..0..2
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..364
• Oh, Seungsang. "Maximal independent sets on a grid graph." Discrete Mathematics 340.12 (2017): 2762-2768. Also arXiv:1709.03678.
• Eric Weisstein's World of Mathematics, Grid Graph
• Eric Weisstein's World of Mathematics, Maximal Independent Vertex Set

Crossrefs

Column 1 is A000931(n+6).

Column 2 is A006355(n+1).

Columns 3-7 are A197049, A197050, A197051, A197052, A197053.

Main diagonal is A197048.

Cf. A089934 (independent sets), A218354 (dominating sets).