%I #4 Nov 30 2012 16:51:38

%S 3,3,6,6,7,10,10,11,21,15,15,17,47,46,21,21,24,129,146,87,28,28,32,

%T 292,621,410,151,36,36,41,600,2190,2645,1069,247,45,45,51,1158,6965,

%U 14536,10350,2701,386,55,55,62,2148,21035,74998,89795,40239,6645,581,66,66,74

%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 nonincreasing columns, 0..2 nXk array

%C Table starts

%C ..3....3......6......10........15........21.........28.........36........45

%C ..6....7.....11......17........24........32.........41.........51........62

%C .10...21.....47.....129.......292.......600.......1158.......2148......3863

%C .15...46....146.....621......2190......6965......21035......60891....171009

%C .21...87....410....2645.....14536.....74998.....371384....1780796...8327951

%C .28..151...1069...10350.....89795....764027....6337533...51044999.398508546

%C .36..247...2701...40239....565824...8017398..113313853.1558416287

%C .45..386...6645..155199...3605746..85092182.2047979807

%C .55..581..15787..581728..22430565.882578607

%C .66..847..36047.2085519.132945658

%C .78.1201..79071.7121374

%C .91.1662.166909

%H R. H. Hardin, <a href="/A219883/b219883.txt">Table of n, a(n) for n = 1..111</a>

%e Some solutions for n=3 k=4

%e ..1..1..0..0....2..2..0..0....1..0..0..0....1..0..0..0....0..0..0..0

%e ..1..1..0..1....2..2..0..0....0..0..0..0....1..0..0..0....0..0..0..0

%e ..1..1..0..0....2..2..0..0....0..0..0..2....2..0..2..0....0..2..0..2

%Y Column 1 is A000217(n+1)

%Y Column 2 is A219589

%Y Row 1 is A000217 for n>1

%Y Row 2 is A046691 for n>2

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ Nov 30 2012