A224281 T(n,k)=Number of nXk 0..3 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.

4, 16, 16, 50, 160, 64, 130, 984, 1600, 256, 296, 4580, 13683, 16000, 1024, 610, 17723, 84132, 186516, 160000, 4096, 1163, 59792, 442089, 1334973, 2596992, 1600000, 16384, 2083, 180821, 2059793, 8073038, 21348990, 37128051, 16000000, 65536, 3544

Offset: 1

Author

R. H. Hardin Apr 02 2013

Keywords

• nonn
• tabl

Comments

Table starts

.......4..........16............50............130.............296

......16.........160...........984...........4580...........17723

......64........1600.........13683..........84132..........442089

.....256.......16000........186516........1334973.........8073038

....1024......160000.......2596992.......21348990.......137489538

....4096.....1600000......37128051......356222482......2425304290

...16384....16000000.....537465766.....6172817040.....45275725025

...65536...160000000....7804602744...109166159263....883012703273

..262144..1600000000..113382138975..1947747629183..17667432461262

.1048576.16000000000.1646661944858.34864494529806.358042017265316

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..199

Crossrefs

Column 1 is A000302

Column 2 is 16*10^(n-1)

Row 1 is A223659

Row 2 is A224058

Formula

Empirical: columns k=1..4 have recurrences of order 1,1,25,52 for n>0,0,26,59

Empirical: rows n=1..6 are polynomials of degree 6*n for k>0,0,3,7,11,15