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A197054 T(n,k)=Number of nXk 0..4 arrays with each element equal to the number of its horizontal and vertical zero neighbors. 14
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 (list; table; graph; refs; listen; history; text; internal format)
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

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

Main diagonal is A197048.

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

Sequence in context: A018119 A177001 A143594 * A120502 A099480 A025783

Adjacent sequences:  A197051 A197052 A197053 * A197055 A197056 A197057

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Oct 09 2011

STATUS

approved

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Last modified July 26 18:16 EDT 2017. Contains 289839 sequences.