%I #4 Nov 29 2014 18:17:35
%S 50,222,336,867,2740,2167,3123,17129,31895,14180,10660,89429,320950,
%T 379440,92429,35064,410718,2482824,6182747,4499219,603249,112373,
%U 1716324,15857764,71431719,119032248,53420941,3935721,353517,6678657,87634164
%N T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with no 2X2 subblock having x11-x00 less than x10-x01
%C Table starts
%C ......50.......222.........867..........3123..........10660...........35064
%C .....336......2740.......17129.........89429.........410718.........1716324
%C ....2167.....31895......320950.......2482824.......15857764........87634164
%C ...14180....379440.....6182747......71431719......641508138......4755605792
%C ...92429...4499219...119032248....2062530658....26192388204....262314968432
%C ..603249..53420941..2295692500...59730054958..1074828860950..14586457826568
%C .3935721.634161915.44280784440.1731036678270.44184817939580.813777827212550
%H R. H. Hardin, <a href="/A251065/b251065.txt">Table of n, a(n) for n = 1..180</a>
%F Empirical for column k:
%F k=1: a(n) = 6*a(n-1) +7*a(n-2) -23*a(n-3) -4*a(n-4) +12*a(n-5)
%F k=2: [order 11]
%F k=3: [order 39]
%F Empirical for row n:
%F n=1: a(n) = 9*a(n-1) -31*a(n-2) +51*a(n-3) -40*a(n-4) +12*a(n-5)
%F n=2: [order 12]
%F n=3: [order 21]
%F n=4: [order 27]
%F n=5: [order 33]
%F n=6: [order 39]
%e Some solutions for n=2 k=4
%e ..1..2..0..2..2....0..1..2..1..1....0..1..1..1..2....1..2..0..0..2
%e ..1..0..2..2..2....0..1..0..2..2....0..0..0..0..2....0..0..2..2..1
%e ..0..1..1..1..1....1..0..1..0..0....0..1..2..2..1....0..1..0..0..1
%Y Column 1 is A184556
%Y Row 1 is A222993(n+1)
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Nov 29 2014