A224310 T(n,k)=Number of nXk 0..2 arrays with diagonals and rows unimodal and antidiagonals nondecreasing

3, 9, 9, 22, 54, 27, 46, 218, 324, 81, 86, 698, 1586, 1944, 243, 148, 1915, 5996, 11361, 11664, 729, 239, 4690, 20214, 45453, 82700, 69984, 2187, 367, 10511, 61953, 164514, 345875, 615481, 419904, 6561, 541, 21919, 174378, 562760, 1258372, 2717759

Offset

1,1

Comments

Table starts

.....3........9.........22..........46..........86..........148..........239

.....9.......54........218.........698........1915.........4690........10511

....27......324.......1586........5996.......20214........61953.......174378

....81.....1944......11361.......45453......164514.......562760......1825800

...243....11664......82700......345875.....1258372......4420701.....15312504

...729....69984.....615481.....2717759.....9829605.....33934344....118317987

..2187...419904....4634768....22071219....80083648....268379906....911404794

..6561..2519424...35003328...182843194...677557164...2215451575...7236130163

.19683.15116544..264487714..1528645389..5882182248..19023816444..59751261572

.59049.90699264.1997888432.12825738594.51821072499.168305254414.512310103541

Links

R. H. Hardin, Table of n, a(n) for n = 1..337

Formula

Empirical for column k:

k=1: a(n) = 3*a(n-1)

k=2: a(n) = 6*a(n-1)

k=3: [order 17]

k=4: [order 30] for n>35

k=5: [order 61] for n>69

k=6: [order 88] for n>98

Empirical: rows n=1..7 are polynomials of degree 4*n for k>0,0,3,6,9,12,15

Example

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

Crossrefs

Column 1 is A000244

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

Row 1 is A223718

Row 2 is A223927

Sequence in context: A183149 A223933 A224057 * A224374 A238323 A223742

Adjacent sequences: A224307 A224308 A224309 * A224311 A224312 A224313

Keyword

nonn,tabl

Author

R. H. Hardin Apr 03 2013

Status

approved