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

1,1

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

Links

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

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

Example

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

Crossrefs

Column 1 is A000244

Column 2 is A000400

Row 1 is A000217(n+1)

Row 2 is A000537(n+1)

Sequence in context: A331841 A223999 A107084 * A224012 A340491 A329511

Adjacent sequences: A224350 A224351 A224352 * A224354 A224355 A224356

Keyword

nonn,tabl

Author

R. H. Hardin Apr 04 2013

Status

approved