login
A223961
T(n,k)=Number of nXk 0..3 arrays with antidiagonals unimodal and rows and diagonals nondecreasing
13
4, 10, 16, 20, 85, 64, 35, 295, 707, 256, 56, 805, 3471, 5864, 1024, 84, 1876, 12311, 41006, 48620, 4096, 120, 3906, 36028, 176893, 485714, 403104, 16384, 165, 7470, 92734, 594286, 2575955, 5777663, 3342081, 65536, 220, 13365, 217144, 1718057
OFFSET
1,1
COMMENTS
Table starts
.......4.........10...........20............35.............56.............84
......16.........85..........295...........805...........1876...........3906
......64........707.........3471.........12311..........36028..........92734
.....256.......5864........41006........176893.........594286........1718057
....1024......48620.......485714.......2575955........9779558.......30643468
....4096.....403104......5777663......37844037......163752797......556027700
...16384....3342081.....68892600.....559416917.....2772658693....10269723035
...65536...27708726....822141033....8299429418....47273211674...191829887779
..262144..229729153...9813968785..123370738379...809416786834..3609049327918
.1048576.1904652103.117159879996.1835707326614.13894273785956.68212899813271
LINKS
FORMULA
Empirical: columns k=1..5 have recurrences of order 1,4,13,34,63 for n>0,0,0,36,68
Empirical rows n=1..7 are polynomials of order 3*n for k>0,0,2,5,8,11,14
EXAMPLE
Some solutions for n=3 k=4
..1..2..2..3....1..2..2..2....0..0..2..2....0..0..1..1....0..1..1..3
..0..2..2..2....1..3..3..3....1..3..3..3....1..2..2..2....0..1..1..1
..0..0..3..3....0..2..3..3....0..3..3..3....1..2..3..3....1..1..2..3
CROSSREFS
Column 1 is A000302
Column 2 is A038235
Row 1 is A000292(n+1)
Sequence in context: A310507 A334115 A265010 * A224391 A224024 A117111
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin Mar 29 2013
STATUS
approved