A223999 T(n,k)=Number of nXk 0..2 arrays with antidiagonals unimodal and rows and diagonals nondecreasing.

3, 6, 9, 10, 31, 27, 15, 76, 157, 81, 21, 155, 476, 793, 243, 28, 281, 1144, 2980, 4004, 729, 36, 469, 2403, 7927, 18672, 20216, 2187, 45, 736, 4614, 17929, 55333, 117386, 102069, 6561, 55, 1101, 8291, 36845, 132119, 388598, 739672, 515338, 19683, 66

Offset: 1

Author

R. H. Hardin Mar 30 2013

Keywords

• nonn
• tabl

Comments

Table starts

.....3........6........10........15.........21.........28..........36

.....9.......31........76.......155........281........469.........736

....27......157.......476......1144.......2403.......4614........8291

....81......793......2980......7927......17929......36845.......71061

...243.....4004.....18672.....55333.....132119.....281271......559188

...729....20216....117386....388598.....984595....2160036.....4368458

..2187...102069....739672...2743444....7400832...16795265....34534687

..6561...515338...4664776..19437479...55978489..131782267...276286000

.19683..2601899..29428242.138010718..425257387.1040869367..2229871293

.59049.13136773.185670484.981047716.3240026429.8260503068.18115082917

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..449

Crossrefs

Column 1 is A000244

Column 2 is A038223

Row 1 is A000217(n+1)

Formula

Empirical: columns k=1..7 have recurrences of order 1,3,9,18,28,39,54 for n>0,0,0,19,31,44,61

Empirical: rows n=1..7 are polynomials of degree 2*n for k>0,0,2,4,6,8,10