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%I #4 Apr 02 2013 06:53:20
%S 3,9,6,22,36,10,46,158,100,15,86,548,648,225,21,148,1600,3096,2017,
%T 441,28,239,4102,12032,12467,5246,784,36,367,9503,40182,59855,41012,
%U 11990,1296,45,541,20299,119367,240829,238366,116692,24842,2025,55,771,40570
%N T(n,k)=Number of nXk 0..2 arrays with rows and antidiagonals unimodal and columns nondecreasing
%C Table starts
%C ..3....9.....22......46.......86.......148........239.........367..........541
%C ..6...36....158.....548.....1600......4102.......9503.......20299........40570
%C .10..100....648....3096....12032.....40182.....119367......322885.......808618
%C .15..225...2017...12467....59855....240829.....850875.....2717731......8000608
%C .21..441...5246...41012...238366...1122522....4542734....16423026.....54399996
%C .28..784..11990..116692...816361...4480391...20568693....82733667....301228048
%C .36.1296..24842..296646..2485967..15921905...83124099...371699763...1478187738
%C .45.2025..47643..688533..6868203..51343083..306179180..1530419762...6671184875
%C .55.3025..85838.1482310.17467782.152072846.1038489172..5835731860..28072690614
%C .66.4356.146878.2995516.41364960.417672794.3266157979.20709405119.110622071553
%H R. H. Hardin, <a href="/A224262/b224262.txt">Table of n, a(n) for n = 1..241</a>
%F Empirical: columns k=1..7 are polynomials of order 2*k for n>0,0,0,2,4,6,8
%F Empirical: rows n=1..7 are polynomials of degree 4*n for k>0,0,0,2,4,6,8
%e Some solutions for n=3 k=4
%e ..1..1..0..0....1..1..1..1....1..1..2..1....0..2..1..0....0..0..0..0
%e ..2..1..1..0....1..2..2..1....2..2..2..1....0..2..1..1....0..0..2..0
%e ..2..2..1..1....2..2..2..1....2..2..2..2....0..2..2..1....0..0..2..2
%Y Column 1 is A000217(n+1)
%Y Column 2 is A000537(n+1)
%Y Row 1 is A223718
%Y Row 2 is A223919
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_ Apr 02 2013
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