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A219686 T(n,k)=Number of nXk arrays of the minimum value of corresponding elements and their horizontal, vertical or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 nXk array.

%I A219686 #6 Jul 23 2025 00:36:29
%S A219686 3,3,3,6,4,6,10,8,9,10,15,14,31,19,15,21,22,87,99,35,21,28,32,208,427,
%T A219686 269,60,28,36,44,452,1531,1688,655,98,36,45,58,922,5031,8964,5726,
%U A219686 1506,154,45,55,74,1799,15763,44736,44816,18486,3356,234,55,66,92,3394,47784
%N A219686 T(n,k)=Number of nXk arrays of the minimum value of corresponding elements and their horizontal, vertical or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 nXk array.
%C A219686 Table starts
%C A219686 ..3...3.....6......10........15.........21.........28..........36.........45
%C A219686 ..3...4.....8......14........22.........32.........44..........58.........74
%C A219686 ..6...9....31......87.......208........452........922........1799.......3394
%C A219686 .10..19....99.....427......1531.......5031......15763.......47784.....140586
%C A219686 .15..35...269....1688......8964......44736.....219216.....1062133....5046678
%C A219686 .21..60...655....5726.....44816.....344926....2709320....21474269..167685059
%C A219686 .28..98..1506...18486....220182....2706117...35011623...461414270.5979059010
%C A219686 .36.154..3356...59458...1116208...22404783..479633094.10451333258
%C A219686 .45.234..7278..189516...5697556..187497531.6609458081
%C A219686 .55.345.15335..589078..28354294.1518906665
%C A219686 .66.495.31362.1771979.135630422
%C A219686 .78.693.62286.5155016
%H A219686 R. H. Hardin, <a href="/A219686/b219686.txt">Table of n, a(n) for n = 1..127</a>
%e A219686 Some solutions for n=3 k=4
%e A219686 ..1..1..1..1....0..0..0..0....1..1..0..0....1..1..0..0....1..1..1..0
%e A219686 ..1..1..1..1....0..0..0..0....1..1..0..0....1..0..0..0....1..1..0..0
%e A219686 ..2..1..1..1....1..1..0..0....2..2..0..0....2..0..0..0....2..2..0..0
%Y A219686 Column 1 and row 1 are A000217 for n>1
%Y A219686 Row 2 is A003682 for n>1
%K A219686 nonn,tabl
%O A219686 1,1
%A A219686 _R. H. Hardin_ Nov 25 2012