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T(n,k)=Number of nXk 0..1 arrays with every repeated value in every row and column greater than or equal to the previous repeated value.
8

%I #4 Jan 20 2016 07:07:54

%S 2,4,4,8,16,8,15,64,64,15,28,225,512,225,28,51,784,3375,3375,784,51,

%T 92,2601,21952,39330,21952,2601,92,164,8464,132651,451278,451278,

%U 132651,8464,164,290,26896,778688,4705642,9116396,4705642,778688,26896,290,509

%N T(n,k)=Number of nXk 0..1 arrays with every repeated value in every row and column greater than or equal to the previous repeated value.

%C Table starts

%C ...2......4.........8..........15.............28...............51

%C ...4.....16........64.........225............784.............2601

%C ...8.....64.......512........3375..........21952...........132651

%C ..15....225......3375.......39330.........451278..........4705642

%C ..28....784.....21952......451278........9116396........163879101

%C ..51...2601....132651.....4705642......163879101.......4977655636

%C ..92...8464....778688....47293550.....2818160392.....143643342651

%C .164..26896...4410944...453985015....45839624169....3885150758271

%C .290..84100..24389000..4225323881...718310821738..100631663710208

%C .509.259081.131872229.38217977443.10874476927778.2504347486850059

%H R. H. Hardin, <a href="/A267735/b267735.txt">Table of n, a(n) for n = 1..180</a>

%F Empirical for column k:

%F k=1: a(n) = 2*a(n-1) +a(n-2) -2*a(n-3) -a(n-4)

%F k=2: [order 9]

%F k=3: [order 16]

%F k=4: [order 42]

%e Some solutions for n=4 k=4

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

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

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

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

%Y Column 1 is A029907(n+1).

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Jan 20 2016