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

1,1

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

Links

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

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

Example

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

Crossrefs

Column 1 is A000244

Column 2 is A038223

Row 1 is A000217(n+1)

Sequence in context: A310141 A348550 A331841 * A107084 A224353 A224012

Adjacent sequences: A223996 A223997 A223998 * A224000 A224001 A224002

Keyword

nonn,tabl

Author

R. H. Hardin Mar 30 2013

Status

approved