A224204 T(n,k)=Number of nXk 0..3 arrays with rows unimodal and antidiagonals nondecreasing.

4, 16, 16, 50, 160, 64, 130, 984, 1600, 256, 296, 4580, 16060, 16000, 1024, 610, 17723, 108625, 263516, 160000, 4096, 1163, 59792, 586343, 2411246, 4357084, 1600000, 16384, 2083, 180821, 2734683, 16355242, 54177872, 72105068, 16000000, 65536

Offset: 1

Author

R. H. Hardin Apr 01 2013

Keywords

• nonn
• tabl

Comments

Table starts

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

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

......64........1600.........16060..........108625...........586343

.....256.......16000........263516.........2411246.........16355242

....1024......160000.......4357084........54177872........451319098

....4096.....1600000......72105068......1229044416......12652618110

...16384....16000000....1193130640.....27957232796.....357890479324

...65536...160000000...19742052632....636184842092...10153767871028

..262144..1600000000..326659600368..14476260508500..288290902851198

.1048576.16000000000.5405039750704.329391607167600.8186391229197618

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..511

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..7 have recurrences of order 1,1,7,10,19,25,41 for n>0,0,0,12,23,32,48

Empirical: rows n=1..7 are polynomials of degree 6*n for k>0,0,0,2,3,4,5