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

1,2

Comments

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

Links

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

Example

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

Crossrefs

Cf. A181018.

Sequence in context: A086327 A114896 A216620 * A066761 A108920 A079405

Adjacent sequences: A181016 A181017 A181018 * A181020 A181021 A181022

Keyword

nonn,tabl

Author

R. H. Hardin, Sep 30 2010

Status

approved