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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 columns, 0..2 nXk array
14

%I #4 Nov 24 2012 08:27:30

%S 3,3,6,6,11,10,10,24,27,15,15,54,130,56,21,21,103,582,566,105,28,28,

%T 178,2109,5072,2134,183,36,36,290,6637,37215,37787,7259,301,45,45,453,

%U 19166,231634,556742,248473,22715,472,55,55,684,51491,1278800,6834071,7236952

%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 columns, 0..2 nXk array

%C Table starts

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

%C ..6...11......24........54.........103...........178...........290

%C .10...27.....130.......582........2109..........6637.........19166

%C .15...56.....566......5072.......37215........231634.......1278800

%C .21..105....2134.....37787......556742.......6834071......72702948

%C .28..183....7259....248473.....7236952.....172829660....3504611581

%C .36..301...22715...1468544....83758183....3863292782..149566037863

%C .45..472...66250...7970617...883579212...78707033574.5869938821256

%C .55..711..181791..40301719..8637866670.1486531293773

%C .66.1035..472662.191514623.79017000203

%C .78.1463.1171147.860805160

%C .91.2016.2778770

%H R. H. Hardin, <a href="/A219627/b219627.txt">Table of n, a(n) for n = 1..111</a>

%e Some solutions for n=3 k=4

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

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

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

%Y Column 1 is A000217(n+1)

%Y Row 1 is A000217 for n>1

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ Nov 24 2012