A223652 - OEIS

%I #4 Mar 25 2013 07:30:34

%S 3,9,5,9,25,13,35,43,169,27,77,229,343,729,60,207,799,5751,1973,3600,

%T 119,513,3237,40981,78213,10425,14161,251,1415,16975,427313,1044311,

%U 1059839,64669,63001,477,4009,58813,4854187,22982345,24559913,13505813,347013

%N T(n,k)=Number of (n+2)Xk 0..1 arrays with all rows having a nonnegative second derivative, and all and columns having a positive second derivative in a quadratic least squares fit, with one and two element arrays taken as having a zero second derivative

%C Table starts

%C ....3........9.........9...........35............77............207

%C ....5.......25........43..........229...........799...........3237

%C ...13......169.......343.........5751.........40981.........427313

%C ...27......729......1973........78213.......1044311.......22982345

%C ...60.....3600.....10425......1059839......24559913.....1119629805

%C ..119....14161.....64669.....13505813.....569451603....50246141433

%C ..251....63001....347013....172509399...13134713511..2434395476789

%C ..477...227529...1639675...1684095249..219299436501.75307144658325

%C .1001..1002001...8731185..20632590041.4713184697381

%C .2011..4044121..47326725.242227127509

%C .4034.16273156.233731602

%C .7901.62425801

%H R. H. Hardin, <a href="/A223652/b223652.txt">Table of n, a(n) for n = 1..96</a>

%e Some solutions for n=3 k=4

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

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

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ Mar 25 2013