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%I #4 Nov 28 2012 17:42:32
%S 4,4,10,10,13,20,20,38,60,35,35,87,394,193,56,56,176,2106,2673,514,84,
%T 84,370,9920,29403,16137,1231,120,120,721,45471,278027,372346,84635,
%U 2748,165,165,1374,186016,2563318,7468429,4032736,413442,5802,220,220,2533
%N T(n,k)=Number of nXk arrays of the minimum value of corresponding elements and their horizontal, diagonal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..3 nXk array
%C Table starts
%C ...4.....4......10........20.........35.........56.........84.........120
%C ..10....13......38........87........176........370........721........1374
%C ..20....60.....394......2106.......9920......45471.....186016......724385
%C ..35...193....2673.....29403.....278027....2563318...20765879...161504901
%C ..56...514...16137....372346....7468429..142482220.2362961573.37398063014
%C ..84..1231...84635...4032736..170199321.6596370468
%C .120..2748..413442..40480756.3570274220
%C .165..5802.1912366.386360710
%C .220.11665.8425696
%C .286.22432
%C .364
%H R. H. Hardin, <a href="/A219828/b219828.txt">Table of n, a(n) for n = 1..71</a>
%e Some solutions for n=3 k=4
%e ..0..0..0..1....0..0..0..1....0..0..2..2....0..0..0..0....0..0..0..3
%e ..0..0..0..0....0..0..0..0....1..0..2..2....0..0..0..0....0..0..0..1
%e ..1..1..0..0....3..1..0..2....2..1..3..2....2..2..1..2....2..0..1..1
%Y Column 1 is A000292(n+1)
%Y Column 2 is A219367
%Y Row 1 is A000292 for n>1
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_ Nov 28 2012
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