%I #4 Jan 15 2014 09:25:24
%S 16,48,48,141,216,141,378,977,977,378,988,3900,6882,3900,988,2482,
%T 15197,41446,41446,15197,2482,6109,55816,242684,375746,242684,55816,
%U 6109,14712,199720,1310058,3328260,3328260,1310058,199720,14712,34896,691634
%N T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with the sum of each 2X2 subblock two median terms lexicographically nondecreasing columnwise and nonincreasing rowwise
%C Table starts
%C ....16......48.......141.........378...........988.............2482
%C ....48.....216.......977........3900.........15197............55816
%C ...141.....977......6882.......41446........242684..........1310058
%C ...378....3900.....41446......375746.......3328260.........26947867
%C ...988...15197....242684.....3328260......44717902........548550245
%C ..2482...55816...1310058....26947867.....548550245......10315124920
%C ..6109..199720...6840001...210973948....6523068739.....190693042666
%C .14712..691634..34087789..1565770379...73498947702....3383470907219
%C .34896.2344746.165068548.11256123354..803300615533...58972454432362
%C .81612.7785110.775598494.78072050576.8465670858075.1000721111089237
%H R. H. Hardin, <a href="/A235765/b235765.txt">Table of n, a(n) for n = 1..127</a>
%F Empirical for column k:
%F k=1: a(n) = 4*a(n-1) -14*a(n-3) +5*a(n-4) +18*a(n-5) -4*a(n-6) -8*a(n-7)
%F k=2: [order 16]
%F k=3: [order 54]
%e Some solutions for n=3 k=4
%e ..0..1..0..1..0....1..1..1..1..0....1..0..0..1..1....0..0..0..0..0
%e ..1..0..1..0..1....0..0..1..1..1....0..1..1..1..0....1..0..1..0..1
%e ..0..0..0..1..1....0..1..0..1..0....0..0..0..0..1....0..0..0..0..0
%e ..0..1..0..0..0....0..0..0..0..0....0..1..0..0..1....0..0..0..1..0
%Y Column 1 is A235541
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Jan 15 2014