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%I #4 Mar 30 2013 11:57:59
%S 4,16,16,50,160,50,130,984,984,130,296,4580,8854,4580,296,610,17723,
%T 58814,58814,17723,610,1163,59792,324702,506513,324702,59792,1163,
%U 2083,180821,1557606,3509115,3509115,1557606,180821,2083,3544,499357,6643979
%N T(n,k)=Number of nXk 0..3 arrays with rows, columns and antidiagonals unimodal and diagonals nondecreasing
%C Table starts
%C ....4......16........50.........130..........296..........610.........1163
%C ...16.....160.......984........4580........17723........59792.......180821
%C ...50.....984......8854.......58814.......324702......1557606......6643979
%C ..130....4580.....58814......506513......3509115.....21167501....114643788
%C ..296...17723....324702.....3509115.....28682690....200974242...1274747540
%C ..610...59792...1557606....21167501....200974242...1573171210..11060805360
%C .1163..180821...6643979...114643788...1274747540..11060805360..83942450048
%C .2083..499357..25596389...564290412...7460451193..72498474377.591725806925
%C .3544.1276595..90177585..2542634801..40485099654.448019196499
%C .5776.3053471.293585050.10557558941.203984697906
%H R. H. Hardin, <a href="/A224064/b224064.txt">Table of n, a(n) for n = 1..112</a>
%F Empirical: columns k=1..5 are polynomials of degree 6*k for n>0,0,3,7,11
%e Some solutions for n=3 k=4
%e ..1..2..2..1....0..0..1..1....0..0..2..2....0..1..0..0....0..1..1..0
%e ..0..2..2..2....0..1..1..1....0..0..2..2....0..2..1..0....0..1..2..2
%e ..0..3..3..2....0..1..1..1....0..0..1..3....1..2..3..1....0..1..2..2
%Y Column 1 is A223659
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_ Mar 30 2013
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