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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. 15
 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

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Last modified March 4 12:21 EST 2024. Contains 370532 sequences. (Running on oeis4.)