%I #4 Dec 03 2012 05:46:56
%S 4,4,4,10,7,10,20,19,20,20,35,43,109,58,35,56,85,479,560,141,56,84,
%T 154,1735,4474,2410,308,84,120,263,5686,29055,32959,9094,637,120,165,
%U 431,17525,172143,381745,204056,32575,1271,165,220,685,51891,983187,4135362
%N T(n,k)=Number of nXk arrays of the minimum value of corresponding elements and their horizontal, vertical or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..3 nXk array
%C Table starts
%C ...4....4......10.......20........35.........56.........84.........120
%C ...4....7......19.......43........85........154........263.........431
%C ..10...20.....109......479......1735.......5686......17525.......51891
%C ..20...58.....560.....4474.....29055.....172143.....983187.....5489377
%C ..35..141....2410....32959....381745....4135362...44269383...470121602
%C ..56..308....9094...204056...4176405...83856137.1708594026.34797091227
%C ..84..637...32575..1209492..45252407.1728522691
%C .120.1271..114987..7316891.519542824
%C .165.2460..396917.44430342
%C .220.4624.1315916
%C .286.8444
%C .364
%H R. H. Hardin, <a href="/A220010/b220010.txt">Table of n, a(n) for n = 1..84</a>
%e Some solutions for n=3 k=4
%e ..2..1..1..1....1..1..1..1....2..1..1..1....3..2..0..0....2..1..0..0
%e ..2..1..1..1....1..1..1..1....2..0..0..1....3..2..0..0....2..0..0..0
%e ..3..2..1..1....3..3..1..1....0..0..0..1....3..3..3..3....3..0..0..0
%Y Column and Row 1 are A000292 for n>1
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_ Dec 03 2012