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%I #4 Dec 30 2014 14:43:19
%S 16,47,47,125,173,125,335,724,735,335,907,3160,4800,3192,907,2470,
%T 13810,31156,30920,13917,2470,6740,60368,200740,305872,199512,60779,
%U 6740,18406,263920,1294016,3006936,3013228,1285960,265605,18406,50278,1153880
%N T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with every 2X2 subblock diagonal maximum minus antidiagonal maximum nondecreasing horizontally, vertically and ne-to-sw antidiagonally
%C Table starts
%C .....16.......47........125..........335............907.............2470
%C .....47......173........724.........3160..........13810............60368
%C ....125......735.......4800........31156.........200740..........1294016
%C ....335.....3192......30920.......305872........3006936.........29746140
%C ....907....13917.....199512......3013228.......44555528........665370612
%C ...2470....60779....1285960.....29779356......664592224......15101198444
%C ...6740...265605....8289288....294392852.....9887498224.....340936886060
%C ..18406..1161035...53433608...2912660356...147292687568....7720152604732
%C ..50278..5075841..344449224..28819853684..2193102920288..174647893015868
%C .137354.22191959.2220470152.285212776212.32661849908016.3953303875494396
%H R. H. Hardin, <a href="/A253350/b253350.txt">Table of n, a(n) for n = 1..361</a>
%F Empirical for column k:
%F k=1: a(n) = 3*a(n-1) -2*a(n-3) for n>6
%F k=2: a(n) = 6*a(n-1) -5*a(n-2) -12*a(n-3) +12*a(n-4) for n>6
%F k=3: [order 7] for n>8
%F k=4: [order 11] for n>14
%F k=5: [order 23] for n>25
%F k=6: [order 43] for n>46
%F k=7: [order 84] for n>87
%F Empirical for row n:
%F n=1: a(n) = 3*a(n-1) -2*a(n-3) for n>6
%F n=2: a(n) = 5*a(n-1) -12*a(n-3) for n>6
%F n=3: [order 7] for n>10
%F n=4: [order 11] for n>15
%F n=5: [order 23] for n>26
%F n=6: [order 43] for n>47
%F n=7: [order 84] for n>88
%e Some solutions for n=3 k=4
%e ..1..0..0..1..1....0..1..0..0..0....0..1..1..1..1....1..1..1..1..1
%e ..1..1..1..1..0....1..1..1..1..1....1..1..1..0..0....0..0..0..1..0
%e ..1..1..1..1..1....1..1..1..1..1....1..1..1..1..1....1..1..1..1..0
%e ..0..0..0..1..0....0..0..1..0..1....0..0..0..0..0....0..0..1..1..0
%Y Column 1 and row 1 are A204609
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Dec 30 2014