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%I #4 Jan 16 2014 07:54:21
%S 81,549,549,3459,8160,3459,20537,112146,110923,20537,118383,1403872,
%T 3294824,1378463,118383,668041,16791083,87473420,87276535,16385455,
%U 668041,3720671,193298612,2193348247,4948377018,2183863895,187651928
%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 columnwise and nonincreasing rowwise
%C Table starts
%C ........81..........549...........3459...........20537...........118383
%C .......549.........8160.........112146.........1403872.........16791083
%C ......3459.......110923........3294824........87473420.......2193348247
%C .....20537......1378463.......87276535......4948377018.....265469754317
%C ....118383.....16385455.....2183863895....264596677243...30753132992706
%C ....668041....187651928....51823058334..13346776888685.3381137131414373
%C ...3720671...2100282123..1185755777410.644799592944959
%C ..20536617..23113626964.26334832022372
%C .112678583.251566008413
%C .615713801
%H R. H. Hardin, <a href="/A235833/b235833.txt">Table of n, a(n) for n = 1..60</a>
%F Empirical for column k:
%F k=1: [linear recurrence of order 14]
%F k=2: [order 84]
%F Empirical for row n:
%F n=1: [linear recurrence of order 14]
%F n=2: [order 84]
%e Some solutions for n=2 k=4
%e ..2..0..0..0..0....2..0..0..2..1....2..0..0..1..0....0..0..0..0..0
%e ..1..1..1..1..1....1..1..1..0..1....1..1..1..2..1....1..1..2..1..1
%e ..2..0..0..1..0....1..1..1..0..1....1..0..1..2..2....2..0..0..0..2
%Y Column 1 and row 1 are A235584
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Jan 16 2014