A223801 T(n,k)=Number of nXk 0..3 arrays with rows and antidiagonals unimodal

4, 16, 16, 50, 256, 64, 130, 2500, 4096, 256, 296, 16900, 110116, 65536, 1024, 610, 87616, 1658703, 4816168, 1048576, 4096, 1163, 372100, 16979881, 151310069, 210163664, 16777216, 16384, 2083, 1352569, 131295500, 2844578252, 13602542576

Offset

1,1

Comments

Table starts

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

......16...........256..............2500................16900

......64..........4096............110116..............1658703

.....256.........65536...........4816168............151310069

....1024.......1048576.........210163664..........13602542576

....4096......16777216........9169032476........1216562667529

...16384.....268435456......400006582368......108631485025292

...65536....4294967296....17450517286804.....9695922803812530

..262144...68719476736...761287955888788...865293308203272685

.1048576.1099511627776.33211580867804324.77218182866179219113

Links

R. H. Hardin, Table of n, a(n) for n = 1..198

Formula

Empirical for column k:

k=1: a(n) = 4*a(n-1)

k=2: a(n) = 16*a(n-1)

k=3: [order 10]

k=4: [order 27]

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

Example

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

Crossrefs

Column 1 is A000302

Column 2 is A001025

Row 1 is A223659

Row 2 is A223756

Sequence in context: A223663 A224113 A223876 * A336938 A232516 A220109

Adjacent sequences: A223798 A223799 A223800 * A223802 A223803 A223804

Keyword

nonn,tabl

Author

R. H. Hardin Mar 27 2013

Status

approved