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%I #4 Dec 07 2012 07:07:11
%S 4,4,4,10,10,10,20,36,38,20,35,89,238,103,35,56,182,956,1013,245,56,
%T 84,333,3294,6855,3916,547,84,120,567,10762,42338,44886,15067,1168,
%U 120,165,918,33804,264239,527350,303148,58288,2395,165,220,1431,101396,1594229
%N T(n,k)=Number of nXk arrays of the minimum value of corresponding elements and their horizontal, vertical or diagonal 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....10......36.......89........182........333........567.........918
%C ..10....38.....238......956.......3294......10762......33804......101396
%C ..20...103....1013.....6855......42338.....264239....1594229.....8996095
%C ..35...245....3916....44886.....527350....6316576...70265746...722552145
%C ..56...547...15067...303148....6896106..154837661.3139823062.59609805010
%C ..84..1168...58288..2089805...89707755.3725275252
%C .120..2395..218422.14021160.1115147627
%C .165..4724..773169.88828793
%C .220..8982.2583728
%C .286.16504
%C .364
%H R. H. Hardin, <a href="/A220204/b220204.txt">Table of n, a(n) for n = 1..84</a>
%e Some solutions for n=3 k=4
%e ..2..2..0..0....2..2..2..2....1..1..0..0....2..0..0..0....0..0..0..0
%e ..2..2..2..0....3..2..2..2....1..1..0..0....3..2..0..0....2..0..0..0
%e ..3..3..2..2....3..3..3..2....3..3..0..0....3..3..1..1....3..3..1..0
%Y Column and Row 1 are A000292 for n>1
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_ Dec 07 2012
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