A179004 T(n,k)=Maximum 1's in an nXk binary array with no element equal to a strict majority of its horizontal and vertical neighbors

1, 1, 1, 2, 2, 2, 2, 4, 4, 2, 3, 4, 5, 4, 3, 4, 6, 7, 7, 6, 4, 4, 6, 9, 9, 9, 6, 4, 5, 8, 10, 11, 11, 10, 8, 5, 6, 8, 12, 13, 14, 13, 12, 8, 6, 6, 10, 14, 16, 17, 17, 16, 14, 10, 6, 7, 10, 15, 18, 20, 20, 20, 18, 15, 10, 7, 8, 12, 17, 20, 22, 24, 24, 22, 20, 17, 12, 8, 8, 12, 19, 22, 26, 27, 28, 27

Offset

1,4

Comments

Conjecture: away from boundaries a sliding 101 pattern would fill with a limiting 2/3 1's

Table starts

..1..1..2..2..3..4..4..5..6..6..7..8..8..9.10.10.11.12.12.13

..1..2..4..4..6..6..8..8.10.10.12.12.14.14.16.16.18.18.20

..2..4..5..7..9.10.12.14.15.17.19.20.22.24.25.27.29.30

..2..4..7..9.11.13.16.18.20.22.25.27.29.31.34.36.38

..3..6..9.11.14.17.20.22.26.28.31.34.37.40.43.45

..4..6.10.13.17.20.24.27.30.34.37.41.44.48.51

..4..8.12.16.20.24.28.32.36.40.44.48.52.56

..5..8.14.18.22.27.32.37.42.46.51.56.60

..6.10.15.20.26.30.36.42.47.52.58

..6.10.17.22.28.34.40.46.52.58

..7.12.19.25.31.37.44.51.58

..8.12.20.27.34.41.48.56

..8.14.22.29.37.44.52

..9.14.24.31.40.48

.10.16.25.34.43

.10.16.27.36

.11.18.29

.12.18

.12

Links

R. H. Hardin, Table of n, a(n) for n = 1..198

Example

Some solutions for 6X6 with maximal 20 1's
..1..1..0..1..0..0....1..1..0..1..0..0....1..1..0..1..0..0....0..1..0..1..0..1
..0..0..1..0..1..1....0..0..1..0..1..1....0..0..1..0..1..1....0..1..1..0..0..1
..1..1..0..1..1..0....1..1..0..1..1..0....1..1..0..1..1..0....1..0..1..1..1..0
..0..1..0..1..0..1....0..1..0..1..0..1....0..1..1..1..0..1....0..1..0..0..1..1
..1..0..1..1..0..0....1..0..1..1..0..1....1..0..0..0..1..0....1..0..1..1..0..0
..1..0..1..0..1..1....1..0..1..0..1..0....1..0..1..1..0..1....1..0..1..0..1..1

Crossrefs

Sequence in context: A119802 A237120 A060369 * A143979 A034877 A224516

Adjacent sequences: A179001 A179002 A179003 * A179005 A179006 A179007

Keyword

nonn,tabl

Author

R. H. Hardin Jan 03 2011

Status

approved