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%I #4 Nov 30 2014 18:33:08
%S 10,25,25,64,86,64,164,310,310,164,421,1135,1654,1135,421,1081,4172,
%T 8976,8976,4172,1081,2776,15353,49104,73170,49104,15353,2776,7129,
%U 56519,268638,599869,599869,268638,56519,7129,18308,208082,1470646,4923412
%N T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with no 2X2 subblock having the minimum of its diagonal elements less than the absolute difference of its antidiagonal elements
%C Table starts
%C ....10......25........64.........164...........421............1081
%C ....25......86.......310........1135..........4172...........15353
%C ....64.....310......1654........8976.........49104..........268638
%C ...164....1135......8976.......73170........599869.........4923412
%C ...421....4172.....49104......599869.......7392190........91120318
%C ..1081...15353....268638.....4923412......91120318......1688254298
%C ..2776...56519...1470646....40413851....1123772109.....31288421074
%C ..7129..208082...8050116...331748759...13857491196....579864211963
%C .18308..766105..44068836..2723267431..170891121600..10746714294838
%C .47017.2820622.241240750.22354871755.2107379861537.199169443650957
%H R. H. Hardin, <a href="/A251201/b251201.txt">Table of n, a(n) for n = 1..799</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-1) +2*a(n-2) -a(n-3) -a(n-4)
%F k=2: a(n) = 2*a(n-1) +7*a(n-2) -a(n-3) -7*a(n-4) -a(n-5) for n>6
%F k=3: [order 9] for n>10
%F k=4: [order 14] for n>16
%F k=5: [order 22] for n>25
%F k=6: [order 35] for n>39
%F k=7: [order 56] for n>61
%e Some solutions for n=4 k=4
%e ..1..1..1..0..1....1..0..1..1..0....1..1..0..1..1....1..0..1..0..1
%e ..1..0..1..1..0....0..1..1..1..1....0..1..1..1..0....0..1..0..1..0
%e ..0..1..0..1..1....1..0..1..1..1....1..1..0..1..1....1..1..1..1..1
%e ..1..0..1..0..1....1..1..1..1..0....0..1..1..1..0....1..1..0..1..1
%e ..0..1..1..1..1....1..1..0..1..1....1..0..1..1..1....1..1..1..1..1
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Nov 30 2014
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