A181019 T(n,k) = maximum number of 1s in an n X k binary matrix with no three 1s adjacent in a line along a row, column or diagonally.

1, 2, 2, 2, 4, 2, 3, 4, 4, 3, 4, 6, 6, 6, 4, 4, 8, 7, 7, 8, 4, 5, 8, 9, 9, 9, 8, 5, 6, 10, 10, 12, 12, 10, 10, 6, 6, 12, 12, 13, 16, 13, 12, 12, 6, 7, 12, 14, 16, 17, 17, 16, 14, 12, 7, 8, 14, 15, 18, 20, 20, 20, 18, 15, 14, 8, 8, 16, 17, 20, 24, 23, 23, 24, 20, 17, 16, 8, 9, 16, 19, 22, 25, 26

Offset: 1

Author

R. H. Hardin, Sep 30 2010

Keywords

• nonn
• tabl

Comments

For the diagonal (square arrays, k = n), see A181018. - M. F. Hasler, Jan 19 2016

Examples

			The table starts:
  1..2..2..3..4..4..5..6..6..7..8..8..9.10.10.11.12.12.13..14..14
  2..4..4..6..8..8.10.12.12.14.16.16.18.20.20.22.24.24.26..28..28
  2..4..6..7..9.10.12.14.15.17.19.20.22.24.25.27.29.30.32..34..35
  3..6..7..9.12.13.16.18.20.22.24.26.28.30.32.34.37.39.41..43..45
  4..8..9.12.16.17.20.24.25.28.32.33.36.40.41.44.48.49.52..56..57
  4..8.10.13.17.20.23.26.29.32.36.38.41.45.48.51.54.57.60..63..66
  5.10.12.16.20.23.26.30.33.37.41.44.48.51.55.58.62.65.69..72..76
  6.12.14.18.24.26.30.36.38.42.48.50.54.60.62.66.72.74.78..84..86
  6.12.15.20.25.29.33.38.42.47.52.56.60.66.70.74.79.83.88..92..96
  7.14.17.22.28.32.37.42.47.52.58.62.67.72.77.82.87.92.98.102.107
The unique maximal solution for 5X5 is the following:
  1..1..0..1..1
  1..1..0..1..1
  0..0..0..0..0
  1..1..0..1..1
  1..1..0..1..1
		

Links

• R. H. Hardin and Peter J. Taylor, Table of n, a(n) for n = 1..496 (first 220 terms from R. H. Hardin)

Crossrefs

Cf. A181018.