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%I #4 Dec 01 2014 13:50:55
%S 10,25,25,61,79,61,149,238,238,149,365,720,890,720,365,894,2199,3369,
%T 3369,2199,894,2189,6717,12859,16006,12859,6717,2189,5360,20484,48980,
%U 76167,76167,48980,20484,5360,13125,62464,186162,361845,451826,361845
%N T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with no 2X2 subblock having the maximum of its diagonal elements greater than the absolute difference of its antidiagonal elements
%C Table starts
%C ....10.....25.......61.......149........365.........894..........2189
%C ....25.....79......238.......720.......2199........6717.........20484
%C ....61....238......890......3369......12859.......48980........186162
%C ...149....720.....3369.....16006......76167......361845.......1720147
%C ...365...2199....12859.....76167.....451826.....2688099......16024915
%C ...894...6717....48980....361845....2688099....20080487.....149982413
%C ..2189..20484...186162...1720147...16024915...149982413....1401489913
%C ..5360..62464...707897...8186775...95495471..1118147932...13088358653
%C .13125.190542..2693783..38968823..568712168..8339278058..122472226217
%C .32139.581259.10250631.185439356.3387770571.62282522930.1147464543755
%H R. H. Hardin, <a href="/A251317/b251317.txt">Table of n, a(n) for n = 1..759</a>
%F Empirical for column k:
%F k=1: a(n) = 3*a(n-1) -2*a(n-2) +2*a(n-3) -a(n-4)
%F k=2: a(n) = 5*a(n-1) -9*a(n-2) +13*a(n-3) -13*a(n-4) +6*a(n-5) -2*a(n-6)
%F k=3: [order 10]
%F k=4: [order 15] for n>17
%F k=5: [order 26] for n>27
%F k=6: [order 42] for n>44
%F k=7: [order 68] for n>70
%e Some solutions for n=4 k=4
%e ..0..1..0..0..1....1..1..1..0..0....0..1..1..0..0....1..1..0..1..1
%e ..0..1..0..0..1....0..0..1..1..0....1..0..1..1..0....0..1..0..0..1
%e ..0..1..0..0..0....1..0..0..1..1....1..1..0..1..1....0..1..0..0..0
%e ..0..1..1..1..1....1..0..0..0..1....0..1..0..0..1....0..1..1..0..0
%e ..0..0..0..0..1....1..1..1..0..0....0..1..0..0..1....0..0..1..1..1
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Dec 01 2014
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