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

Author

R. H. Hardin Mar 29 2013

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A000302

Column 2 is A038235

Row 1 is A000292(n+1)

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