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A224012 T(n,k)=Number of nXk 0..2 arrays with rows nondecreasing and antidiagonals unimodal 12
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 (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........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 * A329511 A065940 A024795

Adjacent sequences:  A224009 A224010 A224011 * A224013 A224014 A224015

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin Mar 30 2013

STATUS

approved

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Last modified February 24 00:51 EST 2020. Contains 332195 sequences. (Running on oeis4.)