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%I #4 Jan 12 2014 05:49:48
%S 16,48,48,141,222,141,378,1049,1049,378,988,4348,8711,4348,988,2482,
%T 17658,61401,61401,17658,2482,6109,67012,429443,758256,429443,67012,
%U 6109,14712,247639,2704866,9618173,9618173,2704866,247639,14712,34896,880814
%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 rowwise and columnwise
%C Table starts
%C ....16.......48........141..........378.............988.............2482
%C ....48......222.......1049.........4348...........17658............67012
%C ...141.....1049.......8711........61401..........429443..........2704866
%C ...378.....4348......61401.......758256.........9618173........108503097
%C ...988....17658.....429443......9618173.......229990437.......4902247081
%C ..2482....67012....2704866....108503097......4902247081.....201871410288
%C ..6109...247639...16395328...1173374675.....99992110087....8016394678681
%C .14712...880814...93093885..11635568187...1844719926176..287100634818875
%C .34896..3061429..508540185.109453308692..31896122665112.9572600813928528
%C .81612.10385988.2659704703.966932051675.509962551465235
%H R. H. Hardin, <a href="/A235548/b235548.txt">Table of n, a(n) for n = 1..112</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 19]
%F k=3: [order 77]
%e Some solutions for n=3 k=4
%e ..1..1..1..0..1....0..0..0..0..1....0..0..1..1..0....1..0..0..1..1
%e ..0..0..0..1..1....0..1..0..0..0....0..0..1..1..1....0..0..0..1..0
%e ..1..1..1..1..1....0..0..1..1..1....0..1..1..0..1....0..1..1..1..0
%e ..1..0..1..1..0....1..0..1..0..1....0..1..1..1..1....1..0..1..0..0
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Jan 12 2014
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