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A219471 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 columns, 0..3 nXk array.

%I A219471 #6 Jul 23 2025 00:30:09
%S A219471 4,4,10,10,23,20,20,68,82,35,35,211,673,239,56,56,547,4838,5040,619,
%T A219471 84,84,1248,28159,87083,32229,1471,120,120,2663,143718,1227441,
%U A219471 1306891,185800,3259,165,165,5432,674954,14696377,43792361,17399442,982456,6800
%N A219471 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 columns, 0..3 nXk array.
%C A219471 Table starts
%C A219471 ...4.....4.......10..........20...........35............56............84
%C A219471 ..10....23.......68.........211..........547..........1248..........2663
%C A219471 ..20....82......673........4838........28159........143718........674954
%C A219471 ..35...239.....5040.......87083......1227441......14696377.....157191488
%C A219471 ..56...619....32229.....1306891.....43792361....1222433026...29873644925
%C A219471 ..84..1471...185800....17399442...1357658929...86755752059.4758315482104
%C A219471 .120..3259...982456...208345624..37552353044.5432184254977
%C A219471 .165..6800..4815782..2285009931.947150536824
%C A219471 .220.13464.22059734.23253970439
%C A219471 .286.25453.95049799
%C A219471 .364.46178
%C A219471 .455
%H A219471 R. H. Hardin, <a href="/A219471/b219471.txt">Table of n, a(n) for n = 1..83</a>
%e A219471 Some solutions for n=3 k=4
%e A219471 ..0..0..0..0....0..0..0..2....0..0..2..2....0..0..1..2....0..0..1..1
%e A219471 ..0..0..0..0....0..0..2..1....0..0..2..0....1..1..2..3....0..0..2..3
%e A219471 ..2..3..0..0....1..1..1..1....0..0..0..0....1..1..2..3....2..3..1..1
%Y A219471 Column 1 is A000292(n+1)
%Y A219471 Row 1 is A000292 for n>1
%Y A219471 Diagonal is A216678
%K A219471 nonn,tabl
%O A219471 1,1
%A A219471 _R. H. Hardin_ Nov 20 2012