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

Author

R. H. Hardin Mar 30 2013

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A000244

Column 2 is A000400

Row 1 is A000217(n+1)

Row 2 is A000537(n+1)

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