

A197054


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


16



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
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OFFSET

1,2


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


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): 27622768. Also arXiv:1709.03678.
Eric Weisstein's World of Mathematics, Grid Graph
Eric Weisstein's World of Mathematics, Maximal Independent Vertex Set


EXAMPLE

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


CROSSREFS

Column 1 is A000931(n+6).
Column 2 is A006355(n+1).
Columns 37 are A197049, A197050, A197051, A197052, A197053.
Main diagonal is A197048.
Cf. A089934 (independent sets), A218354 (dominating sets).
Sequence in context: A143594 A298949 A329097 * A337926 A120502 A099480
Adjacent sequences: A197051 A197052 A197053 * A197055 A197056 A197057


KEYWORD

nonn,tabl


AUTHOR

R. H. Hardin, Oct 09 2011


STATUS

approved



