A223652 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

3, 9, 5, 9, 25, 13, 35, 43, 169, 27, 77, 229, 343, 729, 60, 207, 799, 5751, 1973, 3600, 119, 513, 3237, 40981, 78213, 10425, 14161, 251, 1415, 16975, 427313, 1044311, 1059839, 64669, 63001, 477, 4009, 58813, 4854187, 22982345, 24559913, 13505813, 347013

Offset

1,1

Comments

Table starts

....3........9.........9...........35............77............207

....5.......25........43..........229...........799...........3237

...13......169.......343.........5751.........40981.........427313

...27......729......1973........78213.......1044311.......22982345

...60.....3600.....10425......1059839......24559913.....1119629805

..119....14161.....64669.....13505813.....569451603....50246141433

..251....63001....347013....172509399...13134713511..2434395476789

..477...227529...1639675...1684095249..219299436501.75307144658325

.1001..1002001...8731185..20632590041.4713184697381

.2011..4044121..47326725.242227127509

.4034.16273156.233731602

.7901.62425801

Links

R. H. Hardin, Table of n, a(n) for n = 1..96

Example

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

Crossrefs

Sequence in context: A197023 A096418 A100811 * A077383 A084492 A327762

Adjacent sequences: A223649 A223650 A223651 * A223653 A223654 A223655

Keyword

nonn,tabl

Author

R. H. Hardin Mar 25 2013

Status

approved