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A224353 T(n,k)=Number of nXk 0..2 arrays with diagonals and antidiagonals unimodal and rows nondecreasing 12
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 (list; table; graph; refs; listen; history; text; internal format)
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: A310141 A223999 A107084 * A224012 A329511 A065940

Adjacent sequences:  A224350 A224351 A224352 * A224354 A224355 A224356

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin Apr 04 2013

STATUS

approved

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Last modified December 9 08:20 EST 2019. Contains 329877 sequences. (Running on oeis4.)