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%I #5 Mar 31 2012 12:37:01
%S 81,450,450,2500,4539,2500,11100,44641,44641,11100,49284,312001,
%T 752562,312001,49284,192474,2173565,8183170,8183170,2173565,192474,
%U 751689,12097076,87487117,129062037,87487117,12097076,751689,2707641,67329896
%N T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with the sums of 2X2 subblocks nondecreasing rightwards and downwards
%C Table starts
%C ......81.......450........2500.........11100...........49284...........192474
%C .....450......4539.......44641........312001.........2173565.........12097076
%C ....2500.....44641......752562.......8183170........87487117........694547816
%C ...11100....312001.....8183170.....129062037......2019310610......21958547501
%C ...49284...2173565....87487117....2019310610.....45791699846.....687853333430
%C ..192474..12097076...694547816...21958547501....687853333430...13629970952083
%C ..751689..67329896..5466340007..239090847020..10297878073062..271354063234561
%C .2707641.320850651.34834605810.1998393334223.113754005579615.3835838251329000
%H R. H. Hardin, <a href="/A204230/b204230.txt">Table of n, a(n) for n = 1..111</a>
%e Some solutions for n=4 k=3
%e ..2..2..1..2....0..2..2..0....0..2..2..2....0..0..2..0....2..1..0..2
%e ..1..2..2..2....1..0..1..2....1..2..0..2....0..0..0..1....0..0..2..0
%e ..2..2..1..2....0..2..2..0....0..2..2..2....1..0..2..1....1..2..0..2
%e ..1..2..2..2....2..0..1..2....1..2..1..2....0..2..2..2....1..2..2..2
%e ..2..2..1..2....0..2..2..1....1..2..2..2....0..1..2..1....2..2..1..2
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_ Jan 13 2012