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%I #4 Nov 29 2012 16:42:05
%S 3,3,6,6,7,10,10,17,16,15,15,33,65,33,21,21,56,218,225,62,28,28,86,
%T 591,1302,669,108,36,36,125,1437,5950,6367,1815,177,45,45,173,3195,
%U 23946,48677,28116,4617,276,55,55,230,6668,88110,328442,356688,116212,11125
%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..2 nXk array
%C Table starts
%C ..3....3......6.......10.........15..........21...........28...........36
%C ..6....7.....17.......33.........56..........86..........125..........173
%C .10...16.....65......218........591........1437.........3195.........6668
%C .15...33....225.....1302.......5950.......23946........88110.......303739
%C .21...62....669.....6367......48677......328442......2061724.....12323578
%C .28..108...1815....28116.....356688.....4032388.....43528933....457223032
%C .36..177...4617...116212....2458431....47321720....902318235..17136806921
%C .45..276..11125...452177...16110182...539690445..18538578004.645090935308
%C .55..413..25523..1661479..100697878..5969586828.371652215049
%C .66..597..55964..5791018..602555826.63786858888
%C .78..838.117681.19242699.3462463890
%C .91.1147.238066.61244524
%H R. H. Hardin, <a href="/A219852/b219852.txt">Table of n, a(n) for n = 1..126</a>
%e Some solutions for n=3 k=4
%e ..1..0..0..0....0..0..0..0....1..1..1..1....1..1..0..0....1..0..0..0
%e ..0..0..0..2....0..0..0..1....1..1..1..1....0..0..0..0....1..0..0..0
%e ..0..2..0..0....1..1..1..2....1..1..1..1....0..0..1..2....2..0..0..1
%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 29 2012
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