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%I #4 Jan 15 2014 10:09:00
%S 16,46,46,120,178,120,288,628,628,288,660,1948,2994,1948,660,1456,
%T 5643,12417,12417,5643,1456,3136,15185,47501,70752,47501,15185,3136,
%U 6624,39029,166904,377890,377890,166904,39029,6624,13808,95779,552444,1874171
%N T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with the sum of each 2X2 subblock two extreme terms minus its two median terms lexicographically nondecreasing columnwise and nonincreasing rowwise
%C Table starts
%C ....16.....46......120.......288.........660.........1456..........3136
%C ....46....178......628......1948........5643........15185.........39029
%C ...120....628.....2994.....12417.......47501.......166904........552444
%C ...288...1948....12417.....70752......377890......1874171.......8783904
%C ...660...5643....47501....377890.....2931878.....21858973.....157282139
%C ..1456..15185...166904...1874171....21858973....256515598....3001277411
%C ..3136..39029...552444...8783904...157282139...3001277411...59502624140
%C ..6624..95779..1724793..38884279..1084189363..34219649525.1172336263809
%C .13808.227803..5144350.163704284..7146773223.377305772901
%C .28480.525427.14696712.657363226.45042182253
%H R. H. Hardin, <a href="/A235772/b235772.txt">Table of n, a(n) for n = 1..112</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-1) +4*a(n-2) -8*a(n-3) -4*a(n-4) +8*a(n-5)
%F k=2: [order 15]
%F k=3: [order 37]
%F k=4: [order 88]
%e Some solutions for n=4 k=4
%e ..0..0..0..1..0....0..1..1..0..0....0..0..0..0..0....0..0..0..0..1
%e ..1..1..0..0..0....1..1..1..0..0....0..0..0..0..1....1..1..1..0..0
%e ..0..0..1..1..1....1..0..1..1..1....0..0..0..0..1....0..1..1..0..1
%e ..1..1..1..0..1....1..1..1..0..0....1..1..1..1..1....1..1..0..1..1
%e ..1..0..0..0..0....1..0..1..1..1....0..1..0..1..1....0..1..1..0..1
%Y Column 1 is A235549
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Jan 15 2014
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