A223227 T(n,k)=Number of nXk 0..1 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

2, 4, 4, 5, 16, 5, 11, 25, 25, 11, 19, 121, 48, 121, 19, 37, 361, 280, 280, 361, 37, 68, 1369, 1036, 3926, 1036, 1369, 68, 137, 4624, 4656, 26376, 26376, 4656, 4624, 137, 261, 18769, 21300, 251110, 278904, 251110, 21300, 18769, 261, 547, 68121, 99324

Offset

1,1

Comments

Table starts

....2.......4........5...........11............19..............37

....4......16.......25..........121...........361............1369

....5......25.......48..........280..........1036............4656

...11.....121......280.........3926.........26376..........251110

...19.....361.....1036........26376........278904.........4466304

...37....1369.....4656.......251110.......4466304.......137420222

...68....4624....21300......2272864......67584976......3725574696

..137...18769....99324.....22449494....1093365880....113910021538

..261...68121...447912....215688364...17888793702...3513298650108

..547..299209..2331228...2635210346..382511445066.152586774462250

.1047.1096209.11037718..26127577834.6457494717192

.2085.4347225.54004060.269923989830

Links

R. H. Hardin, Table of n, a(n) for n = 1..127

Example

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

Crossrefs

Sequence in context: A327629 A121528 A243003 * A160904 A306340 A205969

Adjacent sequences: A223224 A223225 A223226 * A223228 A223229 A223230

Keyword

nonn,tabl

Author

R. H. Hardin Mar 18 2013

Status

approved