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

Author

R. H. Hardin Mar 30 2013

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A000302

Column 2 is A011557

Row 1 is A000292(n+1)

Row 2 is A001249

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