A223777 T(n,k)=Number of nXk 0..1 arrays with rows and columns unimodal and antidiagonals nondecreasing

2, 4, 4, 7, 12, 7, 11, 28, 28, 11, 16, 56, 78, 56, 16, 22, 101, 180, 180, 101, 22, 29, 169, 371, 461, 371, 169, 29, 37, 267, 707, 1040, 1040, 707, 267, 37, 46, 403, 1269, 2164, 2516, 2164, 1269, 403, 46, 56, 586, 2170, 4246, 5573, 5573, 4246, 2170, 586, 56, 67

Offset

1,1

Comments

Table starts

..2...4....7....11....16.....22.....29......37......46......56.......67

..4..12...28....56...101....169....267.....403.....586.....826.....1134

..7..28...78...180...371....707...1269....2170....3563....5650.....8692

.11..56..180...461..1040...2164...4246....7950...14308...24877....41945

.16.101..371..1040..2516...5573..11635...23230...44703...83305...150815

.22.169..707..2164..5573..12975..28346...59231..119555..234348...447489

.29.267.1269..4246.11635..28346..64256..138913..290180..589799..1170809

.37.403.2170..7950.23230..59231.138913..308895..662370.1382382..2822162

.46.586.3563.14308.44703.119555.290180..662370.1451996.3093428..6448124

.56.826.5650.24877.83305.234348.589799.1382382.3093428.6707709.14215457

Links

R. H. Hardin, Table of n, a(n) for n = 1..420

Formula

Empirical: columns k=1..7 are polynomials of degree 2*k for n> 0,0,0,1,2,3,4

Example

Some solutions for n=3 k=4
..0..0..1..1....0..0..0..1....0..0..0..0....0..0..0..1....1..0..0..0
..0..1..1..1....0..0..1..1....0..0..0..0....0..1..1..1....0..0..0..0
..1..1..1..0....0..1..1..1....0..0..1..0....1..1..1..1....0..0..0..1

Crossrefs

Column 1 is A000124

Column 2 is A223764

Sequence in context: A297682 A297607 A223770 * A227089 A225900 A227558

Adjacent sequences: A223774 A223775 A223776 * A223778 A223779 A223780

Keyword

nonn,tabl

Author

R. H. Hardin Mar 27 2013

Status

approved