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%I #4 Jan 16 2014 08:21:08
%S 81,487,487,2581,6921,2581,12373,86509,86509,12373,55929,919222,
%T 2919508,919222,55929,241933,8638740,84434218,84434218,8638740,241933,
%U 1015889,73276865,2090202044,7084268884,2090202044,73276865,1015889,4174941
%N T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with the sum of each 2X2 subblock two extreme terms minus its two median terms lexicographically nondecreasing rowwise and columnwise
%C Table starts
%C .......81........487.........2581..........12373...........55929.........241933
%C ......487.......6921........86509.........919222.........8638740.......73276865
%C .....2581......86509......2919508.......84434218......2090202044....44724089619
%C ....12373.....919222.....84434218.....7084268884....509718744920.31142484762646
%C ....55929....8638740...2090202044...509718744920.109676839408289
%C ...241933...73276865..44724089619.31142484762646
%C ..1015889..573836909.849474770590
%C ..4174941.4209526173
%C .16895401
%H R. H. Hardin, <a href="/A235842/b235842.txt">Table of n, a(n) for n = 1..49</a>
%F Empirical for column k:
%F k=1: [linear recurrence of order 16]
%e Some solutions for n=2 k=4
%e ..0..2..0..0..0....0..1..1..0..2....0..1..1..0..1....0..1..0..2..0
%e ..2..2..0..1..2....1..1..1..0..0....1..1..0..0..2....1..0..1..0..0
%e ..1..2..1..1..1....0..0..2..0..2....0..2..0..0..0....1..0..2..2..0
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Jan 16 2014