A224353 T(n,k)=Number of nXk 0..2 arrays with diagonals and antidiagonals unimodal and rows nondecreasing.

3, 6, 9, 10, 36, 27, 15, 100, 216, 81, 21, 225, 788, 1296, 243, 28, 441, 2321, 5880, 7776, 729, 36, 784, 5840, 19608, 45064, 46656, 2187, 45, 1296, 13052, 57387, 160362, 349280, 279936, 6561, 55, 2025, 26610, 151010, 495985, 1351748, 2710892, 1679616

Offset: 1

Author

R. H. Hardin Apr 04 2013

Keywords

• nonn
• tabl

Comments

Table starts

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

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

....27......216........788.......2321........5840.......13052........26610

....81.....1296.......5880......19608.......57387......151010.......363392

...243.....7776......45064.....160362......495985.....1421762......3816783

...729....46656.....349280....1351748.....4231138....12340932.....34697869

..2187...279936....2710892...11704964....37433596...107694133....300892325

..6561..1679616...21021916..102319662...342170839...977742699...2654062881

.19683.10077696..163012744..895494806..3178789749..9202126546..24422915139

.59049.60466176.1264202660.7833508842.29672959682.88363107023.233364588801

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..264

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..6 have recurrences of order 1,1,10,26,56,98

Empirical: rows n=1..7 are polynomials of degree 2*n for k>0,0,1,3,5,7,9