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%I #21 Dec 11 2020 09:56:59
%S 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,
%T 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,
%U 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
%N 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.
%C For the diagonal (square arrays, k = n), see A181018. - _M. F. Hasler_, Jan 19 2016
%H R. H. Hardin and Peter J. Taylor, <a href="/A181019/b181019.txt">Table of n, a(n) for n = 1..496</a> (first 220 terms from R. H. Hardin)
%e The table starts:
%e 1..2..2..3..4..4..5..6..6..7..8..8..9.10.10.11.12.12.13..14..14
%e 2..4..4..6..8..8.10.12.12.14.16.16.18.20.20.22.24.24.26..28..28
%e 2..4..6..7..9.10.12.14.15.17.19.20.22.24.25.27.29.30.32..34..35
%e 3..6..7..9.12.13.16.18.20.22.24.26.28.30.32.34.37.39.41..43..45
%e 4..8..9.12.16.17.20.24.25.28.32.33.36.40.41.44.48.49.52..56..57
%e 4..8.10.13.17.20.23.26.29.32.36.38.41.45.48.51.54.57.60..63..66
%e 5.10.12.16.20.23.26.30.33.37.41.44.48.51.55.58.62.65.69..72..76
%e 6.12.14.18.24.26.30.36.38.42.48.50.54.60.62.66.72.74.78..84..86
%e 6.12.15.20.25.29.33.38.42.47.52.56.60.66.70.74.79.83.88..92..96
%e 7.14.17.22.28.32.37.42.47.52.58.62.67.72.77.82.87.92.98.102.107
%e The unique maximal solution for 5X5 is the following:
%e 1..1..0..1..1
%e 1..1..0..1..1
%e 0..0..0..0..0
%e 1..1..0..1..1
%e 1..1..0..1..1
%Y Cf. A181018.
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Sep 30 2010
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