A224374 T(n,k)=Number of nXk 0..2 arrays with rows unimodal and antidiagonals nondecreasing.

3, 9, 9, 22, 54, 27, 46, 218, 324, 81, 86, 698, 1838, 1944, 243, 148, 1915, 7608, 15540, 11664, 729, 239, 4690, 26314, 77793, 132236, 69984, 2187, 367, 10511, 80819, 311367, 800309, 1126072, 419904, 6561, 541, 21919, 227112, 1092281, 3607078, 8297747

Offset: 1

Author

R. H. Hardin Apr 05 2013

Keywords

• nonn
• tabl

Comments

Table starts

.....3........9.........22..........46...........86...........148

.....9.......54........218.........698.........1915..........4690

....27......324.......1838........7608........26314.........80819

....81.....1944......15540.......77793.......311367.......1092281

...243....11664.....132236......800309......3607078......13831334

...729....69984....1126072.....8297747.....42132769.....174854516

..2187...419904....9588028....86251004....495660330....2231009824

..6561..2519424...81634704...896856330...5848449149...28645726612

.19683.15116544..695055928..9325161494..69064897862..368818252942

.59049.90699264.5917866680.96954549463.815702088065.4752723627808

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..1008

Crossrefs

Column 1 is A000244

Column 2 is 9*6^(n-1)

Row 1 is A223718

Row 2 is A223927

Formula

Empirical: columns k=1..7 have recurrences of order 1,1,5,7,11,14,19 for n>0,0,0,8,13,18,24

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