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

1,1

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

Links

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

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

Example

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

Crossrefs

Column 1 is A000302

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

Row 1 is A223659

Row 2 is A224058

Sequence in context: A224064 A224050 A224281 * A238287 A223811 A223762

Adjacent sequences: A224201 A224202 A224203 * A224205 A224206 A224207

Keyword

nonn,tabl

Author

R. H. Hardin Apr 01 2013

Status

approved