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A220153 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.

%I A220153 #6 Jul 23 2025 00:53:54
%S A220153 3,3,6,6,11,10,10,23,26,15,15,50,77,52,21,21,88,254,242,95,28,28,137,
%T A220153 645,1174,727,163,36,36,197,1413,4559,5410,2062,266,45,45,268,2841,
%U A220153 16110,34959,24684,5493,416,55,55,350,5412,53947,214767,279304,108169,13773
%N A220153 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 A220153 Table starts
%C A220153 ..3....3......6.......10........15.........21..........28..........36
%C A220153 ..6...11.....23.......50........88........137.........197.........268
%C A220153 .10...26.....77......254.......645.......1413........2841........5412
%C A220153 .15...52....242.....1174......4559......16110.......53947......173732
%C A220153 .21...95....727.....5410.....34959.....214767.....1272216.....7244186
%C A220153 .28..163...2062....24684....279304....3057777....32566283...333052410
%C A220153 .36..266...5493...108169...2173203...42648602...822242009.15270635323
%C A220153 .45..416..13773...448881..16032779..564936966.19788620178
%C A220153 .55..627..32664..1761976.111800304.7083618786
%C A220153 .66..915..73654..6564622.739040657
%C A220153 .78.1298.158660.23314449
%C A220153 .91.1796.327852
%H A220153 R. H. Hardin, <a href="/A220153/b220153.txt">Table of n, a(n) for n = 1..111</a>
%e A220153 Some solutions for n=3 k=4
%e A220153 ..0..0..0..0....0..0..0..0....1..1..1..1....0..0..0..0....1..1..1..1
%e A220153 ..0..1..0..0....2..1..0..0....2..1..1..1....1..1..0..0....1..1..0..1
%e A220153 ..0..0..0..1....2..2..1..1....2..2..2..2....1..1..2..2....2..2..0..0
%Y A220153 Column 1 is A000217(n+1)
%Y A220153 Row 1 is A000217 for n>1
%K A220153 nonn,tabl
%O A220153 1,1
%A A220153 _R. H. Hardin_ Dec 06 2012