A224012 T(n,k)=Number of nXk 0..2 arrays with rows nondecreasing and antidiagonals unimodal

3, 6, 9, 10, 36, 27, 15, 100, 216, 81, 21, 225, 868, 1296, 243, 28, 441, 2661, 7378, 7776, 729, 36, 784, 6815, 28541, 62764, 46656, 2187, 45, 1296, 15340, 90051, 297859, 534352, 279936, 6561, 55, 2025, 31324, 245055, 1108969, 3094127, 4549684, 1679616

Offset

1,1

Comments

Table starts

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

.....9.......36........100.........225..........441...........784..........1296

....27......216........868........2661.........6815.........15340.........31324

....81.....1296.......7378.......28541........90051........245055........595822

...243.....7776......62764......297859......1108969.......3516324.......9866389

...729....46656.....534352.....3094127.....13275381......47735665.....150787422

..2187...279936....4549684....32148473....157347899.....630339756....2200064042

..6561..1679616...38737252...334179881...1859567103....8213689391...31256208954

.19683.10077696..329817976..3474343713..21962353421..106375878027..437370837827

.59049.60466176.2808146488.36122604265.259365424097.1373916879120.6067995150599

Links

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

Formula

Empirical: columns k=1..7 have recurrences of order 1,1,5,7,11,14,19

Empirical: rows n=1..7 are polynomials of degree 2*n for k>0,0,1,2,3,4,5

Example

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

Crossrefs

Column 1 is A000244

Column 2 is A000400

Row 1 is A000217(n+1)

Row 2 is A000537(n+1)

Sequence in context: A223999 A107084 A224353 * A340491 A329511 A065940

Adjacent sequences: A224009 A224010 A224011 * A224013 A224014 A224015

Keyword

nonn,tabl

Author

R. H. Hardin Mar 30 2013

Status

approved