%I #4 Feb 16 2014 05:50:16
%S 256,1718,1718,11701,19694,11701,81402,228866,228866,81402,563166,
%T 2744048,4554824,2744048,563166,3880918,32465580,94068938,94068938,
%U 32465580,3880918,26804881,383375880,1903243716,3422869862,1903243716
%N T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with the upper median plus the lower median minus the minimum of every 2X2 subblock differing from its horizontal and vertical neighbors by exactly one
%C Table starts
%C ........256.........1718..........11701...........81402..........563166
%C .......1718........19694.........228866.........2744048........32465580
%C ......11701.......228866........4554824........94068938......1903243716
%C ......81402......2744048.......94068938......3422869862....120261272346
%C .....563166.....32465580.....1903243716....120261272346...7270062501162
%C ....3880918....383375880....38477471800...4232660312790.440610763676048
%C ...26804881...4542257982...782578367787.149839687112404
%C ..185489824..54067139244.16010421948796
%C .1282099556.641031056118
%C .8852862392
%H R. H. Hardin, <a href="/A237936/b237936.txt">Table of n, a(n) for n = 1..60</a>
%F Empirical for column k:
%F k=1: [linear recurrence of order 36]
%e Some solutions for n=2 k=4
%e ..0..3..2..1..3....0..1..2..0..0....0..2..2..1..2....0..0..0..1..2
%e ..0..2..1..0..0....0..2..1..2..2....0..3..3..1..1....2..2..1..3..0
%e ..2..1..2..0..3....0..2..3..3..1....2..1..2..0..3....3..1..0..2..0
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Feb 16 2014