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T(n,k)=Number of nXk 0..3 arrays with every row and column least squares fitting to a nonnegative slope straight line, with a single point array taken as having zero slope
6

%I #4 Mar 16 2013 20:51:52

%S 4,10,10,40,50,40,139,500,500,139,568,3886,20000,3886,568,2134,40380,

%T 540154,540154,40380,2134,8724,359428,22935840,43640576,22935840,

%U 359428,8724,33639,3723640,767019352,6578580741,6578580741,767019352,3723640

%N T(n,k)=Number of nXk 0..3 arrays with every row and column least squares fitting to a nonnegative slope straight line, with a single point array taken as having zero slope

%C Table starts

%C .......4.........10.............40...............139.................568

%C ......10.........50............500..............3886...............40380

%C ......40........500..........20000............540154............22935840

%C .....139.......3886.........540154..........43640576..........6578580741

%C .....568......40380.......22935840........6578580741.......4148524583552

%C ....2134.....359428......767019352......713054874385....1726991116346936

%C ....8724....3723640....32485035360...107232700247240.1085230897885735392

%C ...33639...34904103..1174139120817.12938444501010386

%C ..136904..359369380.49199105599520

%C ..534276.3443215781

%C .2166472

%H R. H. Hardin, <a href="/A223165/b223165.txt">Table of n, a(n) for n = 1..71</a>

%e Some solutions for n=3 k=4

%e ..0..0..0..1....0..0..0..2....0..0..0..2....0..0..0..1....0..0..0..2

%e ..0..0..0..1....0..0..1..0....0..0..2..1....2..2..3..3....0..1..2..1

%e ..2..0..2..2....0..0..2..2....0..3..1..2....0..0..2..3....1..3..3..3

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ Mar 16 2013