%I #4 Mar 16 2013 06:40:53

%S 99,989,989,16089,25929,16089,215563,1328305,1328305,215563,2616383,

%T 55977857,261298801,55977857,2616383,31465359,1853983303,40346506449,

%U 40346506449,1853983303,31465359,363006521,63763662879,4545405907875

%N T(n,k)=Number of (n+2)X(k+2) 0..2 arrays with all rows and columns having a strictly positive second derivative in a quadratic least squares fit

%C Table starts

%C ........99.........989.........16089.........215563.......2616383....31465359

%C .......989.......25929.......1328305.......55977857....1853983303.63763662879

%C .....16089.....1328305.....261298801....40346506449.4545405907875

%C ....215563....55977857...40346506449.22503661157680

%C ...2616383..1853983303.4545405907875

%C ..31465359.63763662879

%C .363006521

%H R. H. Hardin, <a href="/A223157/b223157.txt">Table of n, a(n) for n = 1..30</a>

%e Some solutions for n=1 k=4

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ Mar 16 2013