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

Author

R. H. Hardin Mar 27 2013

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A000302

Column 2 is A001025

Row 1 is A223659

Row 2 is A223756

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