A224024 T(n,k)=Number of nXk 0..3 arrays with rows nondecreasing and antidiagonals unimodal

4, 10, 16, 20, 100, 64, 35, 400, 1000, 256, 56, 1225, 6796, 10000, 1024, 84, 3136, 32523, 112436, 100000, 4096, 120, 7056, 122523, 772683, 1859020, 1000000, 16384, 165, 14400, 387729, 4002738, 17735200, 30756756, 10000000, 65536, 220, 27225, 1074167

Offset

1,1

Comments

Table starts

.......4..........10............20..............35...............56

......16.........100...........400............1225.............3136

......64........1000..........6796...........32523...........122523

.....256.......10000........112436..........772683..........4002738

....1024......100000.......1859020........17735200........120352359

....4096.....1000000......30756756.......403836633.......3491241557

...16384....10000000.....508916456......9186127249......99853876444

...65536...100000000....8420768936....208983591829....2841637297963

..262144..1000000000..139333478144...4754911670136...80738139650660

.1048576.10000000000.2305467501680.108190494364824.2292943314015674

Links

R. H. Hardin, Table of n, a(n) for n = 1..364

Formula

Empirical: columns k=1..7 have recurrences of order 1,1,7,10,19,25,41

Empirical: rows n=1..7 are polynomials of degree 3*n for k>0,0,1,2,3,4,5

Example

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

Crossrefs

Column 1 is A000302

Column 2 is A011557

Row 1 is A000292(n+1)

Row 2 is A001249

Sequence in context: A265010 A223961 A224391 * A117111 A310508 A310509

Adjacent sequences: A224021 A224022 A224023 * A224025 A224026 A224027

Keyword

nonn,tabl

Author

R. H. Hardin Mar 30 2013

Status

approved