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%I #4 Nov 14 2012 21:58:17
%S 3,3,3,6,3,6,10,7,7,10,15,12,37,12,15,21,21,113,113,21,21,28,35,345,
%T 493,345,35,28,36,57,955,2391,2391,955,57,36,45,91,2508,10287,19307,
%U 10287,2508,91,45,55,142,6303,42301,131724,131724,42301,6303,142,55,66,216
%N T(n,k)=Number of nXk arrays of the minimum value of corresponding elements and their horizontal, vertical, diagonal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..2 nXk array
%C Table starts
%C ..3...3......6.......10........15..........21..........28..........36
%C ..3...3......7.......12........21..........35..........57..........91
%C ..6...7.....37......113.......345.........955........2508........6303
%C .10..12....113......493......2391.......10287.......42301......165593
%C .15..21....345.....2391.....19307......131724......854611.....5244065
%C .21..35....955....10287....131724.....1401275....14175675...136413948
%C .28..57...2508....42301....854611....14175675...225464479..3456415362
%C .36..91...6303...165593...5244065...136413948..3456415362.85975478510
%C .45.142..15251...623267..31109196..1283062154.52566495532
%C .55.216..35567..2251824.177926081.11695541948
%C .66.320..80116..7816033.979705264
%C .78.462.174791.26126804
%H R. H. Hardin, <a href="/A219217/b219217.txt">Table of n, a(n) for n = 1..127</a>
%e Some solutions for n=3 k=4
%e ..0..0..0..0....0..0..0..1....1..1..2..2....0..0..1..2....0..0..1..1
%e ..0..0..0..0....0..0..0..1....1..1..1..1....0..0..1..1....0..0..1..1
%e ..0..0..0..2....0..0..1..1....1..1..1..1....1..1..1..1....0..0..2..2
%Y Column 1 is (n^2+n)/2 for n>1
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_ Nov 14 2012