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%I #4 Apr 09 2015 21:34:27
%S 352,1936,1936,9152,14641,9152,43264,81796,81796,43264,189696,456976,
%T 475904,456976,189696,831744,2196324,2768896,2768896,2196324,831744,
%U 3502080,10556001,13278720,16777216,13278720,10556001,3502080,14745600
%N T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with no 3x3 subblock diagonal sum less than the antidiagonal sum
%C Table starts
%C .......352.......1936........9152........43264.......189696........831744
%C ......1936......14641.......81796.......456976......2196324......10556001
%C ......9152......81796......475904......2768896.....13278720......63680400
%C .....43264.....456976.....2768896.....16777216.....80281600.....384160000
%C ....189696....2196324....13278720.....80281600....372556800....1728896400
%C ....831744...10556001....63680400....384160000...1728896400....7780827681
%C ...3502080...46785600...277704000...1648360000...7138454400...30914078976
%C ..14745600..207360000..1211040000...7072810000..29474022400..122825015296
%C ..60702720..878529600..5037021600..28879603600.115996965440..465909995776
%C .249892864.3722098081.20950246564.117920812816.456513732964.1767328289281
%H R. H. Hardin, <a href="/A256771/b256771.txt">Table of n, a(n) for n = 1..336</a>
%F Empirical for column k:
%F k=1: [linear recurrence of order 9]
%F k=2: [order 27]
%F k=3: [order 40]
%F k=4: [order 47]
%F k=5: [same order 47]
%e Some solutions for n=2 k=4
%e ..0..1..0..1..0..0....0..1..0..0..0..0....0..1..0..0..0..1....0..1..0..0..0..0
%e ..1..0..1..0..0..0....0..0..0..0..0..0....1..1..1..0..1..0....1..1..0..1..1..1
%e ..0..0..0..0..0..0....0..0..0..0..0..1....0..0..1..0..1..1....0..1..1..0..1..0
%e ..0..1..1..1..1..1....1..0..1..1..1..1....0..0..0..0..0..0....1..0..0..0..1..1
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Apr 09 2015