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

1,1

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

Links

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

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

Example

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

Crossrefs

Column 1 is A000244

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

Row 1 is A223718

Row 2 is A223927

Sequence in context: A223933 A224057 A224310 * A238323 A223742 A223725

Adjacent sequences: A224371 A224372 A224373 * A224375 A224376 A224377

Keyword

nonn,tabl

Author

R. H. Hardin Apr 05 2013

Status

approved