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%I #4 Nov 19 2012 05:41:06
%S 4,4,4,10,13,10,20,60,60,20,35,193,618,193,35,56,514,4544,4544,514,56,
%T 84,1231,28365,82312,28365,1231,84,120,2748,158473,1205110,1205110,
%U 158473,2748,120,165,5802,811802,15255786,39601472,15255786,811802,5802,165,220
%N T(n,k)=Number of nXk arrays of the minimum value of corresponding elements and their horizontal or vertical 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
%C ...4....13.......60.........193..........514..........1231..........2748
%C ..10....60......618........4544........28365........158473........811802
%C ..20...193.....4544.......82312......1205110......15255786.....174413126
%C ..35...514....28365.....1205110.....39601472....1107664956...28236528076
%C ..56..1231...158473....15255786...1107664956...68107762118.3886911446418
%C ..84..2748...811802...174413126..28236528076.3886911446418
%C .120..5802..3839485..1833703485.667666691778
%C .165.11665.16870880.17851830403
%C .220.22432.69358382
%C .286.41419
%C .364
%H R. H. Hardin, <a href="/A219373/b219373.txt">Table of n, a(n) for n = 1..83</a>
%e Some solutions for n=3 k=4
%e ..0..0..2..3....1..0..0..3....0..0..2..1....0..0..1..2....0..0..1..3
%e ..0..0..0..2....0..0..0..0....0..0..0..1....0..0..2..2....0..1..1..0
%e ..3..0..0..0....2..0..0..1....0..0..0..0....0..0..0..3....3..2..0..0
%Y Column 1 is A000292(n-1) for n>1
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_ Nov 19 2012
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