%I #4 Feb 15 2014 13:47:27

%S 256,1768,1768,12441,21410,12441,88964,265306,265306,88964,636720,

%T 3351086,5825366,3351086,636720,4539422,42195634,130240640,130240640,

%U 42195634,4539422,32392585,529992314,2894506130,5180304200,2894506130

%N T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with the maximum plus the upper median minus the minimum of every 2X2 subblock differing from its horizontal and vertical neighbors by exactly one

%C Table starts

%C .........256..........1768..........12441...........88964..........636720

%C ........1768.........21410.........265306.........3351086........42195634

%C .......12441........265306........5825366.......130240640......2894506130

%C .......88964.......3351086......130240640......5180304200....204201919828

%C ......636720......42195634.....2894506130....204201919828..14245150393666

%C .....4539422.....529992314....64281925312...8050312460472.994081770428554

%C ....32392585....6659762642..1428716811643.317615484901450

%C ...231168380...83778337524.31771479675504

%C ..1651386880.1053822365410

%C .11781707484

%H R. H. Hardin, <a href="/A237904/b237904.txt">Table of n, a(n) for n = 1..60</a>

%F Empirical for column k:

%F k=1: [linear recurrence of order 40] for n>41

%e Some solutions for n=2 k=4

%e ..0..0..2..3..0....0..0..0..2..0....0..0..0..1..0....0..0..3..0..2

%e ..1..2..1..3..2....3..1..2..1..1....3..3..2..2..1....3..1..2..3..2

%e ..2..3..0..0..1....3..1..3..3..0....1..3..2..1..1....1..1..3..1..2

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Feb 15 2014