%I #4 Jan 12 2014 11:23:01

%S 81,549,549,3459,8678,3459,20537,125917,125917,20537,118383,1660676,

%T 4421414,1660676,118383,668041,20719004,140378037,140378037,20719004,

%U 668041,3720671,246491295,4163928036,11284713813,4163928036,246491295

%N T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with the difference of the upper median and minimum value of each 2X2 subblock in lexicographically nondecreasing order rowwise and columnwise

%C Table starts

%C ........81..........549...........3459............20537............118383

%C .......549.........8678.........125917..........1660676..........20719004

%C ......3459.......125917........4421414........140378037........4163928036

%C .....20537......1660676......140378037......11284713813......864122401640

%C ....118383.....20719004.....4163928036.....864122401640...179329543464972

%C ....668041....246491295...114786490439...61249068090242.34988442623259443

%C ...3720671...2840913933..2990032682541.4044723177106236

%C ..20536617..31961677744.74106981549899

%C .112678583.353604367053

%C .615713801

%H R. H. Hardin, <a href="/A235588/b235588.txt">Table of n, a(n) for n = 1..60</a>

%F Empirical for column 1: [linear recurrence of order 14]

%e Some solutions for n=2 k=4

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Jan 12 2014