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%I #4 Mar 31 2013 20:35:31
%S 4,16,10,50,100,20,130,684,400,35,296,3526,4739,1225,56,610,14751,
%T 38561,22988,3136,84,1163,52591,242114,272130,87878,7056,120,2083,
%U 165212,1253770,2335459,1460836,282372,14400,165,3544,468292,5588411,15925611
%N T(n,k)=Number of nXk 0..3 arrays with rows and antidiagonals unimodal and columns nondecreasing
%C Table starts
%C ...4....16.......50.......130.........296..........610...........1163
%C ..10...100......684......3526.......14751........52591.........165212
%C ..20...400.....4739.....38561......242114......1253770........5588411
%C ..35..1225....22988....272130.....2335459.....15925611.......91494280
%C ..56..3136....87878...1460836....16625026....143558572.....1012166273
%C ..84..7056...282372...6425876....95808564...1038484760.....8857798353
%C .120.14400...794220..24197608...468021427...6360047093....65713691148
%C .165.27225..2010035..80350989..1994287334..33901838632...426013124302
%C .220.48400..4668304.240416852..7568051210.160168789130..2451904991177
%C .286.81796.10095924.658890738.25994968917.680269560125.12667946702827
%H R. H. Hardin, <a href="/A224173/b224173.txt">Table of n, a(n) for n = 1..178</a>
%F Empirical: columns k=1..7 are polynomials of degree 3*k for n>0,0,0,3,6,9,12
%F Empirical: rows n=1..5 are polynomials of degree 6*n for k>0,0,0,2,6
%e Some solutions for n=3 k=4
%e ..0..0..1..0....0..0..1..2....0..0..3..0....0..2..0..0....0..3..3..1
%e ..1..3..3..1....0..1..3..2....3..3..3..1....1..2..0..0....1..3..3..1
%e ..1..3..3..3....0..3..3..2....3..3..3..2....2..2..1..0....1..3..3..3
%Y Column 1 is A000292(n+1)
%Y Column 2 is A001249
%Y Row 1 is A223659
%Y Row 2 is A223865
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_ Mar 31 2013
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