A223195 T(n,k)=Number of nXk 0..2 arrays with all rows and columns having a nonnegative second derivative in a quadratic least squares fit, with one and two element arrays taken as having a zero second derivative

3, 9, 9, 16, 81, 16, 50, 256, 256, 50, 138, 2500, 1138, 2500, 138, 387, 19044, 20016, 20016, 19044, 387, 1143, 149769, 252544, 1133664, 252544, 149769, 1143, 3402, 1306449, 3407893, 41164952, 41164952, 3407893, 1306449, 3402, 9948, 11573604

Offset

1,1

Comments

Table starts

.....3.........9..........16............50............138.............387

.....9........81.........256..........2500..........19044..........149769

....16.......256........1138.........20016.........252544.........3407893

....50......2500.......20016.......1133664.......41164952......1615611339

...138.....19044......252544......41164952.....3815358480....386807892609

...387....149769.....3407893....1615611339...386807892609.103879396217927

..1143...1306449....52906752...76015542500.49198404222036

..3402..11573604...807057750.3621550793604

..9948..98962704.12038960562

.30747.945378009

.90018

Links

R. H. Hardin, Table of n, a(n) for n = 1..69

Example

Some solutions for n=3 k=4
..1..0..0..2....1..1..0..1....1..1..0..0....1..2..1..2....1..0..1..1
..1..0..1..0....0..0..1..1....1..0..0..0....0..1..0..1....1..1..0..0
..1..1..2..2....2..2..2..2....2..1..0..1....0..0..0..2....2..2..0..1

Crossrefs

Sequence in context: A110759 A063750 A143225 * A203600 A099720 A183149

Adjacent sequences: A223192 A223193 A223194 * A223196 A223197 A223198

Keyword

nonn,tabl

Author

R. H. Hardin Mar 18 2013

Status

approved