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T(n,k) = Number of (n+1) X (k+1) 0..1 arrays with the determinants of 2 X 2 subblocks nondecreasing rightwards and downwards.
9

%I #9 Jul 15 2014 08:23:25

%S 16,47,47,125,181,125,335,749,749,335,907,3254,4901,3254,907,2470,

%T 14199,31805,31805,14199,2470,6740,62031,205117,313597,205117,62031,

%U 6740,18406,271125,1322417,3084029,3084029,1322417,271125,18406,50278,1185255

%N T(n,k) = Number of (n+1) X (k+1) 0..1 arrays with the determinants of 2 X 2 subblocks nondecreasing rightwards and downwards.

%C Table starts:

%C ....16......47......125........335..........907..........2470............6740

%C ....47.....181......749.......3254........14199.........62031..........271125

%C ...125.....749.....4901......31805.......205117.......1322417.........8522985

%C ...335....3254....31805.....313597......3084029......30487865.......301345617

%C ...907...14199...205117....3084029.....45645661.....681254361.....10133992449

%C ..2470...62031..1322417...30487865....681254361...15468240213....349154906413

%C ..6740..271125..8522985..301345617..10133992449..349154906413..11909737623605

%C .18406.1185255.54938417.2981578169.150976448169.7906679632133.408218289321933

%H R. H. Hardin, <a href="/A204616/b204616.txt">Table of n, a(n) for n = 1..480</a>

%e Some solutions for n=4, k=3:

%e ..1..0..1..1....0..1..0..1....0..1..0..0....0..0..1..0....1..0..1..1

%e ..0..0..0..0....0..0..0..1....0..1..0..0....1..0..0..0....1..0..1..1

%e ..0..1..1..0....1..0..0..0....0..1..0..1....0..0..0..1....0..0..1..1

%e ..0..0..0..0....1..0..0..0....0..1..0..0....0..0..0..1....1..0..0..0

%e ..1..1..1..1....1..0..0..0....0..1..0..0....0..0..0..0....1..0..0..0

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Jan 17 2012