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%I #4 Nov 26 2012 05:35:35
%S 4,4,10,10,13,20,20,45,44,35,35,125,297,129,56,56,283,1751,1860,338,
%T 84,84,561,7862,23506,9674,813,120,120,1030,30452,223069,245205,46026,
%U 1822,165,165,1776,106421,1797459,4745284,2326019,207161,3840,220,220,2916
%N T(n,k)=Number of nXk arrays of the minimum value of corresponding elements and their horizontal 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
%C ..10....13.......45.........125..........283...........561..........1030
%C ..20....44......297........1751.........7862.........30452........106421
%C ..35...129.....1860.......23506.......223069.......1797459......13042996
%C ..56...338.....9674......245205......4745284......79167008....1202223210
%C ..84...813....46026.....2326019.....90220424....3084196884...97254386205
%C .120..1822...207161....21036433...1658836014..118470103282.7921920681423
%C .165..3840...881386...180509639..29601803957.4513018690558
%C .220..7665..3529403..1458287494.504486635692
%C .286.14578.13308249.11082376729
%C .364.26557.47441049
%C .455.46556
%H R. H. Hardin, <a href="/A219714/b219714.txt">Table of n, a(n) for n = 1..96</a>
%e Some solutions for n=3 k=4
%e ..2..2..2..2....2..0..0..0....1..1..0..0....2..2..0..0....1..1..1..1
%e ..2..2..2..2....0..0..0..3....1..1..0..0....2..1..0..0....1..1..1..0
%e ..2..2..2..3....0..2..2..2....2..2..0..2....2..1..0..3....3..0..0..0
%Y Column 1 is A000292(n+1)
%Y Row 1 is A000292 for n>1
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_ Nov 26 2012