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T(n,k)=Number of nXk arrays of the minimum value of corresponding elements and their horizontal or diagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 nXk array
14

%I #4 Dec 06 2012 05:46:22

%S 3,3,6,6,11,10,10,23,26,15,15,50,77,52,21,21,88,254,242,95,28,28,137,

%T 645,1174,727,163,36,36,197,1413,4559,5410,2062,266,45,45,268,2841,

%U 16110,34959,24684,5493,416,55,55,350,5412,53947,214767,279304,108169,13773

%N T(n,k)=Number of nXk arrays of the minimum value of corresponding elements and their horizontal or diagonal 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...11.....23.......50........88........137.........197.........268

%C .10...26.....77......254.......645.......1413........2841........5412

%C .15...52....242.....1174......4559......16110.......53947......173732

%C .21...95....727.....5410.....34959.....214767.....1272216.....7244186

%C .28..163...2062....24684....279304....3057777....32566283...333052410

%C .36..266...5493...108169...2173203...42648602...822242009.15270635323

%C .45..416..13773...448881..16032779..564936966.19788620178

%C .55..627..32664..1761976.111800304.7083618786

%C .66..915..73654..6564622.739040657

%C .78.1298.158660.23314449

%C .91.1796.327852

%H R. H. Hardin, <a href="/A220153/b220153.txt">Table of n, a(n) for n = 1..111</a>

%e Some solutions for n=3 k=4

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

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

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

%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_ Dec 06 2012