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T(n,k)=Number of nX(k+1) 0..2 arrays with every row least squares fitting to a positive slope straight line and every column least squares fitting to a zero or positive slope straight line, with a single point array taken as having zero slope
6

%I #4 Mar 19 2013 09:55:34

%S 3,9,6,36,36,18,102,340,324,41,343,1914,12240,1845,123,996,13850,

%T 195228,221346,17343,310,3159,79266,4750550,8514450,8909352,119660,

%U 957,9237,523133,78948936,576481773,1004831988,221358126,1139787,2530,28755

%N T(n,k)=Number of nX(k+1) 0..2 arrays with every row least squares fitting to a positive slope straight line and every column least squares fitting to a zero or positive slope straight line, with a single point array taken as having zero slope

%C Table starts

%C ....3.......9.........36.........102..........343............996..........3159

%C ....6......36........340........1914........13850..........79266........523133

%C ...18.....324......12240......195228......4750550.......78948936....1652577147

%C ...41....1845.....221346.....8514450....576481773....23314034430.1290079956663

%C ..123...17343....8909352..1004831988.241636868781.29530598586528

%C ..310..119660..221358126.65367672572

%C ..957.1139787.8788947912

%C .2530.8607060

%C .7848

%H R. H. Hardin, <a href="/A223309/b223309.txt">Table of n, a(n) for n = 1..50</a>

%e Some solutions for n=3 k=4

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

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

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

%Y Column 1 is A222856

%Y Row 2 is A222925

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ Mar 19 2013