A223961 T(n,k)=Number of nXk 0..3 arrays with antidiagonals unimodal and rows and diagonals nondecreasing

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

R. H. Hardin, Table of n, a(n) for n = 1..287

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

Adjacent sequences: A223958 A223959 A223960 * A223962 A223963 A223964

Keyword

nonn,tabl

Author

R. H. Hardin Mar 29 2013

Status

approved