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%I #4 Dec 30 2014 19:59:46
%S 81,450,450,2500,3111,2500,11100,22877,22631,11100,49284,148389,
%T 219438,103572,49284,192474,945748,2000385,1027387,521009,192474,
%U 751689,5125790,17316309,10639450,5829147,1977416,751689,2707641,27587386,128407497
%N T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with every 2X2 subblock sum nondecreasing horizontally, vertically and antidiagonally ne-to-sw
%C Table starts
%C .....81.....450.....2500.....11100......49284......192474.......751689
%C ....450....3111....22877....148389.....945748.....5125790.....27587386
%C ...2500...22631...219438...2000385...17316309...128407497....912012350
%C ..11100..103572..1027387..10639450..105139503...943840336...8129400162
%C ..49284..521009..5829147..70942616..811079978..8802760516..90160819133
%C .192474.1977416.21245477.263498334.3064820088.35861948220.395423995297
%H R. H. Hardin, <a href="/A253375/b253375.txt">Table of n, a(n) for n = 1..83</a>
%F Empirical for column k:
%F k=1: [linear recurrence of order 23]
%F k=2: [order 45]
%F k=3: [same order 45] for n>48
%F k=4: [same order 45] for n>53
%F k=5: [same order 45] for n>61
%F k=6: [same order 45] for n>67
%F Empirical for row n:
%F n=1: [linear recurrence of order 23]
%F n=2: [order 79]
%e Some solutions for n=2 k=4
%e ..0..2..0..1..0....1..0..0..0..1....0..0..0..1..1....0..0..0..0..1
%e ..1..0..1..1..2....0..0..1..2..1....0..0..1..0..2....0..0..1..0..1
%e ..1..1..1..1..2....0..1..1..2..2....1..0..1..2..1....0..2..1..2..1
%Y Column 1 and row 1 are A204223
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Dec 30 2014
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