login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (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

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

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: 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 2 05:15 EDT 2022. Contains 357191 sequences. (Running on oeis4.)