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%I #7 Jul 18 2024 08:48:51
%S 4,4,4,10,13,10,20,51,59,20,35,132,415,181,35,56,277,1866,2234,469,56,
%T 84,514,7036,18564,10226,1107,84,120,881,24679,140884,154271,43194,
%U 2447,120,165,1429,82431,1052190,2399643,1230906,175054,5120,165,220,2225,262218
%N T(n,k) is the number of n X k arrays of the minimum value of corresponding elements and their horizontal or vertical neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..3 n X k array.
%C Table starts:
%C ...4.....4......10.......20........35.........56........84........120.......165
%C ...4....13......51......132.......277........514.......881.......1429......2225
%C ..10....59.....415.....1866......7036......24679.....82431.....262218....794994
%C ..20...181....2234....18564....140884....1052190...7579137...51585784.331270888
%C ..35...469...10226...154271...2399643...37870076.572032559.8149176569
%C ..56..1107...43194..1230906..40957383.1391739384
%C ..84..2447..175054..9838834.712907937
%C .120..5120..681294.77121132
%C .165.10197.2520724
%C .220.19415
%C .286
%H R. H. Hardin, <a href="/A219578/b219578.txt">Table of n, a(n) for n = 1..71</a>
%e Some solutions for n=3 and k=4:
%e ..2..1..1..0....1..0..0..0....1..0..0..0....0..0..0..0....2..2..0..0
%e ..3..1..0..0....2..1..0..0....0..0..0..0....2..0..0..0....2..1..1..0
%e ..3..3..1..0....3..3..2..0....3..0..3..1....2..2..2..1....3..3..1..2
%Y Column 1 and Row 1 are A000292 for n>1.
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Nov 23 2012
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