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A223309 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.

%I A223309 #6 Jul 23 2025 03:59:21
%S A223309 3,9,6,36,36,18,102,340,324,41,343,1914,12240,1845,123,996,13850,
%T A223309 195228,221346,17343,310,3159,79266,4750550,8514450,8909352,119660,
%U A223309 957,9237,523133,78948936,576481773,1004831988,221358126,1139787,2530,28755
%N A223309 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 A223309 Table starts
%C A223309 ....3.......9.........36.........102..........343............996..........3159
%C A223309 ....6......36........340........1914........13850..........79266........523133
%C A223309 ...18.....324......12240......195228......4750550.......78948936....1652577147
%C A223309 ...41....1845.....221346.....8514450....576481773....23314034430.1290079956663
%C A223309 ..123...17343....8909352..1004831988.241636868781.29530598586528
%C A223309 ..310..119660..221358126.65367672572
%C A223309 ..957.1139787.8788947912
%C A223309 .2530.8607060
%C A223309 .7848
%H A223309 R. H. Hardin, <a href="/A223309/b223309.txt">Table of n, a(n) for n = 1..50</a>
%e A223309 Some solutions for n=3 k=4
%e A223309 ..2..0..0..1..2....0..0..1..0..1....0..0..0..0..1....0..0..0..0..1
%e A223309 ..1..2..2..2..2....0..1..1..1..2....1..0..1..2..1....0..0..0..1..1
%e A223309 ..2..0..1..1..2....1..0..2..0..2....0..1..1..2..1....0..1..0..1..2
%Y A223309 Column 1 is A222856
%Y A223309 Row 2 is A222925
%K A223309 nonn,tabl
%O A223309 1,1
%A A223309 _R. H. Hardin_ Mar 19 2013