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

Author

R. H. Hardin Apr 03 2013

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A000244

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

Row 1 is A223718

Row 2 is A223927

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